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Math Problems
Precalculus
Find probabilities using the binomial distribution
Approximately
20
%
20\%
20%
of newborns are born more than
1
1
1
week before their due date. A random sample of
20
20
20
newborns is selected.
\newline
The standard deviation of the sampling distribution for the proportion of your sample that is born more than
7
7
7
days before their due date is
\newline
(A)
0.20
0.20
0.20
\newline
(B)
3.2
3.2
3.2
\newline
(C)
0.089
0.089
0.089
\newline
(D)
0.008
0.008
0.008
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The table below shows length of time that customer take to pay their invoices
\newline
\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|}
\newline
\hline \begin{tabular}{l}
\newline
Number of \\
\newline
days
\newline
\end{tabular} &
1
−
9
1-9
1
−
9
&
10
−
19
10-19
10
−
19
&
20
−
29
20-29
20
−
29
&
30
−
39
30-39
30
−
39
&
40
−
49
40-49
40
−
49
&
50
−
59
50-59
50
−
59
&
60
−
69
60-69
60
−
69
&
70
−
79
70-79
70
−
79
&
80
−
89
80-89
80
−
89
&
90
−
99
90-99
90
−
99
\\
\newline
\hline \begin{tabular}{l}
\newline
Number of \\
\newline
Customers
\newline
\end{tabular} &
7
7
7
&
16
16
16
&
22
22
22
&
18
18
18
&
23
23
23
&
9
9
9
&
5
5
5
&
3
3
3
&
2
2
2
&
1
1
1
\\
\newline
\hline
\newline
\end{tabular}
\newline
Use the data above to construct a grouped frequency table with the following column headings:
\newline
i. Class boundaries
\newline
ii. Class mid-points
\newline
iii. Cumulative frequency
\newline
iv. Draw a Histogram to represent the distribution
\newline
v. Draw a Cumulative Frequency Curve for the distribution.
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Krystal Ramirez
\newline
2024
2024
2024
\newline
Question
4
4
4
,
8
8
8
.
2
2
2
.
11
11
11
-T
\newline
HW Score:
42.86
%
,
3
42.86 \%, 3
42.86%
,
3
of
7
7
7
points
\newline
Part
4
4
4
of
5
5
5
\newline
Points:
0
0
0
of
1
1
1
\newline
Save
\newline
ose a simple random sample of size
h
=
200
\mathrm{h}=200
h
=
200
is obtained from a population whose size is
N
=
20
,
000
\mathrm{N}=20,000
N
=
20
,
000
and whose population proportion with a specified characteristic is
p
=
0.6
p=0.6
p
=
0.6
. lete parts (a) through (c) below.
\newline
Not normal because
n
≤
0.05
N
n \leq 0.05 \mathrm{~N}
n
≤
0.05
N
and
n
p
(
1
−
p
)
≥
10
n p(1-p) \geq 10
n
p
(
1
−
p
)
≥
10
.
\newline
Approximately normal because
n
≤
0.05
N
n \leq 0.05 \mathrm{~N}
n
≤
0.05
N
and
n
p
(
1
−
p
)
<
10
n p(1-p)<10
n
p
(
1
−
p
)
<
10
.
\newline
Not normal because
n
≤
0.05
N
n \leq 0.05 \mathrm{~N}
n
≤
0.05
N
and
n
p
(
1
−
p
)
<
10
n p(1-p)<10
n
p
(
1
−
p
)
<
10
.
\newline
Approximately normal because
n
≤
0.05
N
n \leq 0.05 \mathrm{~N}
n
≤
0.05
N
and
n
p
(
1
−
p
)
≥
10
n p(1-p) \geq 10
n
p
(
1
−
p
)
≥
10
.
\newline
mine the mean of the sampling distribution of
h
=
200
\mathrm{h}=200
h
=
200
2
2
2
.
\newline
6
6
6
(Round to one decimal place as needed.)
\newline
mine the standard deviation of the sampling distribution of
h
=
200
\mathrm{h}=200
h
=
200
2
2
2
.
\newline
03464
03464
03464
(Round to six decimal places as fleeded.)
\newline
hat is the probability of obtaining
h
=
200
\mathrm{h}=200
h
=
200
4
4
4
or more individuals with the characteristic? That is, what is
h
=
200
\mathrm{h}=200
h
=
200
5
5
5
?
\newline
h
=
200
\mathrm{h}=200
h
=
200
6
6
6
(Round to four decimal places as needed.)
\newline
Get more help
\newline
Clear all
\newline
Check answe
\newline
e
\newline
h
=
200
\mathrm{h}=200
h
=
200
7
7
7
\newline
53
53
53
.
85
85
85
\newline
Mean:
h
=
200
\mathrm{h}=200
h
=
200
8
8
8
\newline
h
=
200
\mathrm{h}=200
h
=
200
8
8
8
Std. Dev.:
052915
052915
052915
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At a local restaurant, the amount of time that customers have to wait for their food is normally distributed with a mean of
18
18
18
minutes and a standard deviation of
2
2
2
minutes. What is the probability that a randomly selected customer will have to wait less than
15
15
15
minutes, to the nearest thousandth?
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In a company there are
9
9
9
executives:
3
3
3
women and
6
6
6
men. Three are selected at random to attend a management seminar. Find these probabilities. All three selected will be women. Round your answer to five decimal places. The probability that all three people selected will be women is
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A random sample of
200
200
200
students was asked to sample a new type of pizza that the school was considering using as a replacement for the current pizza. Each student stated if they were a freshman, sophomore, junior, or senior and also if they liked the new pizza more than the current pizza (or not). The school would like to know if there is a relationship between grade level and pizza opinion.
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SP
7
7
7
.
4
4
4
\newline
Raina planted yellow and green squash in her vegetable garden. Then she recorded the length of each squash that she harvested.
\newline
\begin{tabular}{|c|c|c|}
\newline
\hline \multicolumn{
3
3
3
}{|c|}{ Length of Yollow Squash
(
c
m
)
(\mathrm{cm})
(
cm
)
} \\
\newline
\hline
8
8
8
&
10
10
10
&
16
16
16
\\
\newline
\hline
8
8
8
&
12
12
12
&
14
14
14
\\
\newline
\hline
18
18
18
&
20
20
20
&
6
6
6
\\
\newline
\hline
\newline
\end{tabular}
\newline
\begin{tabular}{|c|c|c|}
\newline
\hline \multicolumn{
3
3
3
}{|c|}{ Length of Green Squash (cm) } \\
\newline
\hline
14
14
14
&
14
14
14
&
16
16
16
\\
\newline
\hline
12
12
12
&
14
14
14
&
13
13
13
\\
\newline
\hline
16
16
16
&
13
13
13
&
14
14
14
\\
\newline
\hline
\newline
\end{tabular}
\newline
1
1
1
. Make a box plot for each data set. Use the number lines provided below.
\newline
2
2
2
. Which type of Raina's squash has a higher median length based on the box plots?
\newline
3
3
3
. Based on the box plots, which type of Raina's squash would you infer has a more consistent length? Explain your reasoning.
\newline
4
4
4
. Based on the box plots, which type of Raina's squash would you infer is generally shorter? Explain your reasoning.
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1
1
1
. a) John Doe is tied to an elastic cord and is suspended in the air at rest
50
m
50\,\text{m}
50
m
above the ground. He grabs the cord and raises himself
4
m
4\,\text{m}
4
m
up at time
t
=
0
t=0
t
=
0
. If he let go of the rope, he returns to the highest position in
1.2
s
1.2\,\text{s}
1.2
s
, determine the height of John Doe above the ground at
t
=
0.7
s
t=0.7\,\text{s}
t
=
0.7
s
rounded to
2
2
2
decimal places. b) Sketch a nicely labelled cosine graph for
2
2
2
cycles.
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Isabel has a spinner with slices labeled red, green, and blue. She spins the spinner a number of times and each time records the slice on which the spinner lands. The graph shows the results.
\newline
Spin result
\newline
Find Isabel's relative frequency of spinning green or blue. Write your answer as a simplified fraction.
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A consulting firm has
10
10
10
partners in the firm. Mrs Wendytia, the managing partner want to discuss an idea of moving the main office from Central Jakarta to BSD, South Tangerang. Of those
10
10
10
partners,
8
8
8
live in West Jakarta and
2
2
2
live in East Jakarta. She will appoint a committee randomly consist of
3
3
3
partners to have a study about this plan. What is the probability that the committee chosen consist of
2
2
2
partner live in East Jakarta and the others in West Jakarta?
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Euriana Covilhă
\newline
Can I create a Tree Diagram?
\newline
Time:
\newline
9
9
9
:
56
56
56
\newline
Submit Assessment
\newline
Padraic is playing a game with his friend, Radnor. Padraic rolls a
4
4
4
sided die twice. If Padraic rolls at least a
3
3
3
on either roll, then Radnor gives him
1
1
1
gobstopper, otherwise, Padraic has to give Radnor
1
1
1
gobstopper.
\newline
Let's give the label
A
\mathrm{A}
A
to the event that Padraic rolls at least a
3
\mathbf{3}
3
on either roll. What is the probability of this event?
\newline
14
14
14
\newline
5
/
16
5 / 16
5/16
\newline
answered
\newline
Flag for later
\newline
Previous
\newline
6
6
6
of
16
16
16
\newline
Next
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Braden bought new equipment for his bowling alley, including a ball return machine. There is a
66
%
66\%
66%
chance that the machine returns a bowling ball with the finger holes facing up. If the machine returns
5
5
5
bowling balls, what is the probability that exactly
4
4
4
will have the finger holes facing up? Write your answer as a decimal rounded to the nearest thousandth. ____
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Danielle and her teammates are each chewing a piece of tropical flavored gum before their championship softball game.
86
%
86\%
86%
of the pieces are pineapple flavored.
\newline
If
3
3
3
of her teammates are chosen at random, what is the probability that
0
0
0
are chewing pineapple gum?
\newline
Write your answer as a decimal rounded to the nearest thousandth.
\newline
____
\newline
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Last year, Melissa came in
2
2
2
nd place in her school's Spelling Bee. This year, she plans to win
1
1
1
st place. She compiled a long list of words to study,
49
%
49\%
49%
of which have a Latin root.
\newline
If Melissa randomly chooses a word to study from the list
5
5
5
different times this month, what is the probability that exactly
2
2
2
of the words have a Latin root?
\newline
Write your answer as a decimal rounded to the nearest thousandth.
\newline
____
\newline
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56
%
56\%
56%
of students in a class have black hair. If
5
5
5
students are chosen at random, what is the probability that exactly
2
2
2
have black hair? Write your answer as a decimal rounded to the nearest thousandth. ____
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Some friends are taking turns spinning a toy to see how it lands. The toy has four sides, each with a different animal displayed. The toy is weighted unevenly, so that it lands on the turtle
21
%
21\%
21%
of the time. If one of the friends spins the toy
2
2
2
times, what is the probability that it lands on the turtle exactly
2
2
2
times? Write your answer as a decimal rounded to the nearest thousandth. ____
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This Friday, Tucker has a French vocabulary test as well as a Spanish vocabulary test. To prepare, he made a study card for each word,
44
%
44\%
44%
of which are French. Every time he picks a card, he sticks it back in the deck and shuffles again.
\newline
If Tucker picks a study card from the deck
5
5
5
times during his first study session, what is the probability that exactly
3
3
3
cards have a French word?
\newline
Write your answer as a decimal rounded to the nearest thousandth.
\newline
____
\newline
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Last year, Khalil came in
2
2
2
nd place in his school's Spelling Bee. This year, he plans to win
1
1
1
st place. He compiled a long list of words to study,
51
%
51\%
51%
of which have a Latin root.
\newline
If Khalil randomly chooses a word to study from the list
2
2
2
different times this month, what is the probability that
0
0
0
of the words have a Latin root?
\newline
Write your answer as a decimal rounded to the nearest thousandth.
\newline
____
\newline
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It is believed that
71
%
71\%
71%
of tickets purchased for an upcoming music festival are actually legitimate tickets. The rest are fake tickets sold by scam artists. Assume everyone who bought a ticket shows up at the concert.
\newline
If security guards at the festival randomly select
5
5
5
tickets to examine in more detail, what is the probability that exactly
4
4
4
of the tickets are legitimate?
\newline
Write your answer as a decimal rounded to the nearest thousandth.
\newline
____
\newline
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Last year, Ashley came in
2
2
2
nd place in her school's Spelling Bee. This year, she plans to win
1
1
1
st place. She compiled a long list of words to study,
23
%
23\%
23%
of which have a Latin root.
\newline
If Ashley randomly chooses a word to study from the list
5
5
5
different times this month, what is the probability that exactly
3
3
3
of the words have a Latin root?
\newline
Write your answer as a decimal rounded to the nearest thousandth.
\newline
____
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\newline
65
%
65\%
65%
of cows on a farm are pregnant.
\newline
If
2
2
2
cows are chosen at random, what is the probability that exactly
1
1
1
is pregnant?
\newline
Write your answer as a decimal rounded to the nearest thousandth.
\newline
____
\newline
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It is believed that
71
%
71\%
71%
of tickets purchased for an upcoming music festival are actually legitimate tickets. The rest are fake tickets sold by scam artists. Assume everyone who bought a ticket shows up at the concert.
\newline
If security guards at the festival randomly select
2
2
2
tickets to examine in more detail, what is the probability that exactly
2
2
2
of the tickets are legitimate?
\newline
Write your answer as a decimal rounded to the nearest thousandth.
\newline
____
\newline
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Bonnie created a website where users could randomly generate a ＂strong password.＂ She claims that
69
%
69\%
69%
of generated passwords contain at least one capital letter, number, and symbol.
\newline
If the claim is correct, and a user randomly generates
2
2
2
passwords on the website, what is the probability that
0
0
0
of the passwords contain at least one capital letter, number, and symbol?
\newline
Write your answer as a decimal rounded to the nearest thousandth.
\newline
____
\newline
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An art museum recently discovered that
19
%
19\%
19%
of their paintings had been stolen and replaced with replicas. If a tourist observes
2
2
2
different paintings at random, what is the probability that exactly
1
1
1
is a fake? Write your answer as a decimal rounded to the nearest thousandth.____
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palindrome is a number which reads the same backward as forward. For example,
232
232
232
,
4774
4774
4774
,
6
6
6
are palindromes. It is known that a six-digit palindrome is divisible by
75
75
75
, and the quotient is still a palindrome. Find the quotient.
\newline
Answer:
□
\square
□
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Equation for the approximate line of best fit :
y
=
6
7
x
+
2
2
7
y=\frac{6}{7} x+2 \frac{2}{7}
y
=
7
6
x
+
2
7
2
\newline
14
14
14
) Predict the cost of
8
8
8
pounds of strawtoemes.
\newline
- Graph prediction:
\qquad
in
9
9
9
\newline
- Equolion prodection
:
19414
: 19414
:
19414
show your work:
\newline
6
7
⋅
8
+
2
2
7
\frac{6}{7} \cdot 8+2 \frac{2}{7}
7
6
⋅
8
+
2
7
2
\newline
15
15
15
) Predict the cost of
14
14
14
pounds of strawberries.
\newline
- Graph prediction :
1
/
4.50
1 / 4.50
1/4.50
\newline
- Equation prediction :
$
4.29
\$ 4.29
$4.29
Show your work:
\newline
6
7
⋅
14
+
2
2
7
\frac{6}{7} \cdot 14+2 \frac{2}{7}
7
6
⋅
14
+
2
7
2
\newline
16
16
16
) What does the slope of the line of best fit mean in the context of the given situalion is the slope reasonable in this situgtion?
\qquad
are about even above and below the slope.
\qquad
\newline
\qquad
\newline
\qquad
\newline
\qquad
What does the
\qquad
0
0
0
-intercept of the line of best fit mean in the context of the given situation? Is the y-intercept reasonable in this situation?
\qquad
\newline
\qquad
\newline
02015
02015
02015
lindsav Perme
\newline
wuw.lindsayperfo.com
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Coronary bypass surgery: The Agency for Healthcare Research and Quality reported that
60
%
60 \%
60%
of people who had coronary bypass surgery in a recent year were over the age of
65
65
65
, Fifteen coronary bypass patients are sampled. Round the answers to at least four decimal places.
\newline
Part:
0
/
4
0 / 4
0/4
\newline
Part
1
1
1
of
4
4
4
\newline
(a) What is the probability that exactly
10
10
10
of them are over the age of
65
65
65
?
\newline
The probability that exactly
10
10
10
of them are over the age of
65
65
65
is
□
\square
□
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At a science museum, visitors can compete to see who has a faster reaction time. Competitors watch a red screen, and the moment they see it turn from red to green, they push a button. The machine records their reaction times and also asks competitors to report their gender.
\newline
\begin{tabular}{|l|c|c|}
\newline
\cline {
2
2
2
-
3
3
3
} & Male & Female \\
\newline
\hline Less than
0
0
0
.
3
3
3
seconds &
3
3
3
&
5
5
5
\\
\newline
\hline
0
0
0
.
3
3
3
to
0
0
0
.
7
7
7
seconds &
5
5
5
&
2
2
2
\\
\newline
\hline
\newline
\end{tabular}
\newline
What is the probability that a randomly selected competitor reacted in less than
0
0
0
.
3
3
3
seconds and was female?
\newline
Simplify any fractions.
\newline
□
\square
□
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11
11
11
Here is a decimal:
5.020020002000020000020000002
…
5.020020002000020000020000002 \ldots
5.020020002000020000020000002
…
\newline
Arun says:
\newline
There is a regular pattern: one zero, then two zeros, then three zeros, and so on. This is a rational number.
\newline
a Is Arun correct? Give a reason for your answer.
\newline
b Compare your answer with a partner's. Do you agree? If not, who is correct?
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Mr. and Mrs. Doran have a genetic history such that the probability that a child being born to them with a certain trait is
2
2
2
/
9
9
9
. If they have three children, what is the probability that exactly one of their three children will have that trait? Round your answer to the nearest thousandth.
\newline
Answer:
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If a fair coin is tossed
7
7
7
times, what is the probability, to the nearest thousandth, of getting exactly
5
5
5
tails?
\newline
Answer:
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If the probability that the Islanders will beat the Rangers in a game is
1
/
6
1 / 6
1/6
, what is the probability that the Islanders will win exactly five out of six games in a series against the Rangers? Round your answer to the nearest thousandth.
\newline
Answer:
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During a single day at radio station WMZH, the probability that a particular song is played is
0
0
0
.
25
25
25
. What is the probability that this song will be played on exactly
6
6
6
days out of
6
6
6
days? Round your answer to the nearest thousandth.
\newline
Answer:
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Mr. and Mrs. Doran have a genetic history such that the probability that a child being born to them with a certain trait is
7
/
8
7 / 8
7/8
. If they have five children, what is the probability that exactly three of their five children will have that trait? Round your answer to the nearest thousandth.
\newline
Answer:
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The Hiking Club plans to go camping in a State park where the probability of rain on any given day is
31
%
31 \%
31%
. What is the probability that it will rain on exactly three of the four days they are there? Round your answer to the nearest thousandth.
\newline
Answer:
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The Hiking Club plans to go camping in a State park where the probability of rain on any given day is
0
0
0
.
64
64
64
. What is the probability that it will rain on exactly one of the six days they are there? Round your answer to the nearest thousandth.
\newline
Answer:
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The Hiking Club plans to go camping in a State park where the probability of rain on any given day is
3
/
7
3 / 7
3/7
. What is the probability that it will rain on exactly zero of the five days they are there? Round your answer to the nearest thousandth.
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During a single day at radio station WMZH, the probability that a particular song is played is
1
/
6
1 / 6
1/6
. What is the probability that this song will be played on exactly
3
3
3
days out of
4
4
4
days? Round your answer to the nearest thousandth.
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During a single day at radio station WMZH, the probability that a particular song is played is
0
0
0
.
68
68
68
. What is the probability that this song will be played on exactly
2
2
2
days out of
5
5
5
days? Round your answer to the nearest thousandth.
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During a single day at radio station WMZH, the probability that a particular song is played is
2
/
3
2 / 3
2/3
. What is the probability that this song will be played on exactly
2
2
2
days out of
5
5
5
days? Round your answer to the nearest thousandth.
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During a single day at radio station WMZH, the probability that a particular song is played is
0
0
0
.
52
52
52
. What is the probability that this song will be played on at least
5
5
5
days out of
7
7
7
days? Round your answer to the nearest thousandth.
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The Hiking Club plans to go camping in a State park where the probability of rain on any given day is
64
%
64 \%
64%
. What is the probability that it will rain on at most two of the six days they are there? Round your answer to the nearest thousandth.
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Answer:
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If a fair die is rolled
6
6
6
times, what is the probability, rounded to the nearest thousandth, of getting at most
1
1
1
six?
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The Hiking Club plans to go camping in a State park where the probability of rain on any given day is
5
/
6
5 / 6
5/6
. What is the probability that it will rain on at least five of the seven days they are there? Round your answer to the nearest thousandth.
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If a fair die is rolled
7
7
7
times, what is the probability, rounded to the nearest thousandth, of getting at most
1
1
1
six?
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If a fair coin is tossed
7
7
7
times, what is the probability, rounded to the nearest thousandth, of getting at most
1
1
1
tails?
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Mr. and Mrs. Doran have a genetic history such that the probability that a child being born to them with a certain trait is
0
0
0
.
48
48
48
. If they have four children, what is the probability that at most two of their four children will have that trait? Round your answer to the nearest thousandth.
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During a single day at radio station WMZH, the probability that a particular song is played is
1
/
3
1 / 3
1/3
. What is the probability that this song will be played on at most
2
2
2
days out of
4
4
4
days? Round your answer to the nearest thousandth.
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Answer:
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If a fair coin is tossed
9
9
9
times, what is the probability, rounded to the nearest thousandth, of getting at least
7
7
7
heads?
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Answer:
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If the probability that the Islanders will beat the Rangers in a game is
67
%
67 \%
67%
, what is the probability that the Islanders will win at least four out of seven games in a series against the Rangers? Round your answer to the nearest thousandth.
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