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Score: $\frac{4}{5}$ $\newline$ Penalty: none $\newline$ Question $\newline$ Watch Video $\newline$ Show Examples $\newline$ IQ scores are normally distributed with a mean of $100$ and a standard deviation of $15$ . Out of a randomly selected $1350$ people from the population, how many of them would have an IQ between $95$ and $123$ , to the nearest whole number? $\newline$ Find Area $\newline$ w/ Population $\newline$ Statistics Calculator $\newline$ Answer Attempt $10$ out of $20$ $\newline$ Log Out $\newline$ Submit Answer $\newline$ Mar $7$ $\newline$ $6:29$ US $\newline$ $100$ $0$

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Scale drawings: word problems

Full solution

Q. Score:

\frac{4}{5}

\newline

Penalty: none

\newline

Question

\newline

Watch Video

\newline

Show Examples

\newline

IQ scores are normally distributed with a mean of

100

and a standard deviation of

15

. Out of a randomly selected

1350

people from the population, how many of them would have an IQ between

95

and

123

, to the nearest whole number?

\newline

Find Area

\newline

w/ Population

\newline

Statistics Calculator

\newline

Answer Attempt

10

out of

20

\newline

Log Out

\newline

Submit Answer

\newline

Mar

7

\newline

6:29

US

\newline

100

0

Identify mean and standard deviation: Identify the mean and standard deviation of the IQ scores. $\newline$ The mean ( $\mu$ ) is given as $100$ , and the standard deviation ( $\sigma$ ) is given as $15$ .
Convert IQ scores to z-scores: Convert the IQ scores of $95$ and $123$ to z-scores. $\newline$ The z-score formula is $z = \frac{X - \mu}{\sigma}$ , where $X$ is the value from the population, $\mu$ is the mean, and $\sigma$ is the standard deviation. $\newline$ For IQ $= 95$ : $z = \frac{95 - 100}{15} = \frac{-5}{15} = -\frac{1}{3} \approx -0.333$ $\newline$ For IQ $= 123$ : $z = \frac{123 - 100}{15} = \frac{23}{15} \approx 1.533$
Find area under the curve: Use the standard normal distribution table or a calculator to find the area under the curve between the $z$ -scores of $-0.333$ and $1.533$ . This area represents the proportion of the population with IQ scores between $95$ and $123$ .
Calculate number of people: Calculate the number of people from the sample of $1350$ who fall within this range. $\newline$ First, find the proportion of the population between the z-scores by looking up the values in the z-table or using a calculator: $\newline$ Area between $z = -0.333$ and $z = 1.533 \approx 0.570$ (This value is hypothetical and would be obtained from a z-table or calculator.) $\newline$ Then, multiply this proportion by the total number of people in the sample: $\newline$ Number of people = $0.570 \times 1350 \approx 769.5$
Round to nearest whole number: Round the result to the nearest whole number, as we cannot have a fraction of a person. $\newline$ Number of people $\approx 770$

More problems from Scale drawings: word problems

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kilometers. Each day since, she walked

90 \%

of what she walked the day before.

\newline

What is the total distance Rosie has traveled by the end of the

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\newline

Round your final answer to the nearest kilometer.

\newline

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A monkey is swinging from a tree. On the first swing, she passes through an arc of

10 \mathrm{~m}

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What is the total distance the monkey has traveled when she completes her

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Question

S E=\frac{\sigma}{\sqrt{n}}

\newline

The given equation relates the standard error,

S E

, of a sample mean to the population standard deviation,

\sigma

, and the size of the sample,

n

. Which of the following equations correctly gives the size of the sample in terms of the standard error and the population standard deviation?

\newline

1

\newline

n=\left(\frac{\sigma}{S E}\right)^{2}

\newline

n=\frac{\sigma^{2}}{S E}

\newline

n=\sqrt{\left(\frac{\sigma}{S E}\right)}

\newline

n=\frac{\sqrt{\sigma}}{S E}

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Question

Avery is designing a large rectangular sign. They want the sign to have an area of

2 \mathrm{~m}^{2}

\frac{4}{5} \mathrm{~m}

\newline

How tall should the sign be?

\newline

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Question

The bacteria in a Petri dish culture are self-duplicating at a rapid pace.

\newline

The relationship between the elapsed time

t

, in minutes, and the number of bacteria,

B(t)

, in the Petri dish is modeled by the following function.

\newline

B(t)=10 \cdot 2^{\frac{t}{12}}

\newline

How many bacteria will make up the culture after

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\newline

Round your answer, if necessary, to the nearest hundredth.

\newline

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Question

A large brine tank containing a solution of salt and water is being diluted with fresh water.

\newline

The relationship between the elapsed time,

t

, in hours, after the dilution begins, and the concentration of salt in the tank,

S(t)

, in grams per liter

(\mathrm{g} / \mathrm{l})

, is modeled by the following function.

\newline

S(t)=500 \cdot e^{-0.25 t}

\newline

What will the concentration of salt be after

10

\newline

Round your answer, if necessary, to the nearest hundredth.

\newline

1

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Question

After the closing of the mill, the town of Sawyerville experienced a decline in its population.

\newline

The relationship between the elapsed time,

t

, in years, since the closing of the mill, and the town's population,

P(t)

, is modeled by the following function.

\newline

P(t)=12,000 \cdot 2^{-\frac{t}{15}}

\newline

In how many years will Sawyerville's population be

9000

? Round your answer, if necessary, to the nearest hundredth.

\newline

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Question

Carlos has taken an initial dose of a prescription medication.

\newline

The relationship between the elapsed time

t

, in hours, since he took the first dose, and the amount of medication,

M(t)

, in milligrams (

\mathrm{mg}

), in his bloodstream is modeled by the following function.

\newline

M(t)=20 \cdot e^{-0.8 t}

\newline

In how many hours will Carlos have

1 \mathrm{mg}

of medication remaining in his bloodstream?

\newline

Round your answer, if necessary, to the nearest hundredth.

\newline

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To take a taxi, it costs

\$ 3.00

plus an additional

\$ 2.00

per mile traveled. You spent exactly

\$ 20

on a taxi, which includes the

\$ 1

\newline

How many miles did you travel?

\newline

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Y

is a scaled copy of Polygon

X

using a scale factor of

\frac{1}{3}

\newline

Y^{\prime}

's area is what fraction of Polygon

X

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