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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 22 minutes and a standard deviation of 3 minutes. If you visit that restaurant 37 times this year, what is the expected number of times that you would expect to wait between 19 minutes and 23 minutes, to the nearest whole number?
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Snow Examples $\newline$ signment (B-Day) $\newline$ ve: March $7$ at $11$ : $00$ PM $\newline$ Grade: $89 \%$ $\newline$ $\checkmark$ Normai vistribution - rina $<$ score $\newline$ $\checkmark$ Normal Distribution - Empirical Rule $\newline$ $\checkmark$ Normal Distribution - Find Area $\newline$ Normal Distribution w/ Population Size $\newline$ Calculator $\newline$ Danaya Woodruff $\newline$ At a local restaurant, the amount of time that customers have to wait for their food is normally distributed with a mean of $22$ minutes and a standard deviation of $3$ minutes. If you visit that restaurant $37$ times this year, what is the expected number of times that you would expect to wait between $19$ minutes and $23$ minutes, to the nearest whole number? $\newline$ Statistics Calculator $\newline$ Submit Answer

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Identify discrete and continuous random variables

Full solution

Q. Snow Examples

\newline

signment (B-Day)

\newline

ve: March

7

at

11

:

00

PM

\newline

Grade:

89 \%

\newline

\checkmark

Normai vistribution - rina

<

score

\newline

\checkmark

Normal Distribution - Empirical Rule

\newline

\checkmark

Normal Distribution - Find Area

\newline

Normal Distribution w/ Population Size

\newline

Calculator

\newline

Danaya Woodruff

\newline

At a local restaurant, the amount of time that customers have to wait for their food is normally distributed with a mean of

22

minutes and a standard deviation of

3

minutes. If you visit that restaurant

37

times this year, what is the expected number of times that you would expect to wait between

19

minutes and

23

minutes, to the nearest whole number?

\newline

Statistics Calculator

\newline

Submit Answer

Given Information: We are given that the wait time for food at a local restaurant is normally distributed with a mean $\mu$ of $22$ minutes and a standard deviation $\sigma$ of $3$ minutes. We want to find the probability of waiting between $19$ and $23$ minutes.
Standardize Wait Times: First, we need to standardize the wait times of $19$ minutes and $23$ minutes using the z-score formula: $z = (X - \mu) / \sigma$ , where $X$ is the value from the normal distribution, $\mu$ is the mean, and $\sigma$ is the standard deviation.
Calculate z-score for $19$ minutes: Calculate the z-score for $19$ minutes: $z = (19 - 22) / 3 = -3 / 3 = -1$ .
Calculate z-score for $23$ minutes: Calculate the z-score for $23$ minutes: $z = \frac{23 - 22}{3} = \frac{1}{3} \approx 0.33$ .
Lookup z-scores in table: Now, we look up these $z$ -scores in the standard normal distribution table or use a calculator to find the probabilities. The probability of $z$ being less than $-1$ is approximately $0.1587$ , and the probability of $z$ being less than $0.33$ is approximately $0.6293$ .
Find probability of waiting: To find the probability of waiting between $19$ and $23$ minutes, we subtract the probability of waiting less than $19$ minutes from the probability of waiting less than $23$ minutes: $P(19 < X < 23) = P(X < 23) - P(X < 19) = 0.6293 - 0.1587 = 0.4706$ .
Calculate expected number of times: Now, we multiply this probability by the number of visits to find the expected number of times you would wait between $19$ and $23$ minutes: Expected number of times = Total visits $\times$ Probability = $37 \times 0.4706$ .
Round to nearest whole number: Calculate the expected number of times: Expected number of times = $37 \times 0.4706 \approx 17.4122$ .
Round to nearest whole number: Calculate the expected number of times: Expected number of times = $37 \times 0.4706 \approx 17.4122$ .Since we cannot visit a fraction of a time, we round to the nearest whole number: Expected number of times $\approx 17$ (to the nearest whole number).

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\newline

g(c)=-3

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c

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\newline

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c

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1

\newline

g(c)=3

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c

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