Questions: The average amount of money that people spend at Don Mcalds fast food place is 7.1700 with a standard deviation of 1.7200. 50 customers are randomly selected. Please answer the following questions, and round all answers to 4 decimal places where possible and assume a normal distribution. a. What is the distribution of X? X-N(7.17, 1) c. What is the distribution of ∑x? ∑x-N(358.5, 12.1622) d. What is the probability that one randomly selected customer will spend more than 57.3552? 0.4594 e. For the 50 customers, find the probability that their average spent is less than 7.3452. 0.7643 f. Find the probability that the randomly selected 50 customers will spend more than 367.2600. 0.2357 g. For part e) and f), is the assumption of normal necessary? Yes No all groups of 50 people who h. The owner of Don Mcalds gives a coupon for a free sundae to the 4th, at least how much must a group of 50 spend in total to get the free sundae? 379.7923

The average amount of money that people spend at Don Mcalds fast food place is 7.1700 with a standard deviation of 1.7200. 50 customers are randomly selected. Please answer the following questions, and round all answers to 4 decimal places where possible and assume a normal distribution.
a. What is the distribution of X? X-N(7.17, 1)
c. What is the distribution of ∑x? ∑x-N(358.5, 12.1622)
d. What is the probability that one randomly selected customer will spend more than 57.3552? 0.4594
e. For the 50 customers, find the probability that their average spent is less than 7.3452. 0.7643
f. Find the probability that the randomly selected 50 customers will spend more than 367.2600. 0.2357
g. For part e) and f), is the assumption of normal necessary? Yes No all groups of 50 people who
h. The owner of Don Mcalds gives a coupon for a free sundae to the 4th, at least how much must a group of 50 spend in total to get the free sundae? 379.7923
Transcript text: The average amount of money that people spend at Don Mcalds fast food place is $\$ 7.1700$ with a standard deviation of $\$ 1.7200 .50$ customers are randomly selected. Please answer the following questions, and round all answers to 4 decimal places where possible and assume a normal distribution. a. What is the distribution of $X$ ? $X-N(7.17 \quad \checkmark, 1) 0^{\circ}$ c. What is the distribution of $\sum x$ ? $\sum x-N(358.5 \quad \checkmark, 12.1622) \sigma^{6}$ d. What is the probability that one randomly selected customer will spend more than 57.3552 ? 0.4594 ${ }^{\circ}$ e. For the 50 customers, find the probability that their average spent is less than $\$ 7.3452$. $0.7643 \quad \checkmark{ }^{\circ}$ f. Find the probability that the randomly selected 50 customers will spend more than $\$ 367.2600$. 0.2357 $\checkmark \sigma^{\circ}$ g. For part e) and $f$ ), is the assumption of normal necessary? O Yes $\odot$ No all groups of 50 people who h. The owner of Don Mcalds gives a coupon for a free sundae to the 4 , it least how much must a group of 50 spend in total to get the free sundae? $379.7923$
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Solution

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What is the distribution of \( X \)?

Distribution of \( X \)

The distribution of \( X \) is given by \( X \sim N(7.17, 1.72) \).

\(\boxed{X \sim N(7.17, 1.72)}\)

What is the distribution of \( \sum x \)?

Distribution of \( \sum x \)

The distribution of \( \sum x \) is given by \( \sum x \sim N(358.5, 12.1622) \).

\(\boxed{\sum x \sim N(358.5, 12.1622)}\)

What is the probability that one randomly selected customer will spend more than \( 7.3552 \)?

Calculation of probability

The probability that one randomly selected customer will spend more than \( 7.3552 \) is \( P(X > 7.3552) = 1 - P(X \leq 7.3552) = 0.4571 \).

\(\boxed{0.4571}\)

For the 50 customers, find the probability that their average spent is less than \( 7.3452 \).

Calculation of average probability

The probability that the average spent by 50 customers is less than \( 7.3452 \) is \( P(\bar{X} < 7.3452) = 0.7643 \).

\(\boxed{0.7643}\)

Find the probability that the randomly selected 50 customers will spend more than \( 367.2600 \).

Calculation of total spending probability

The probability that the 50 customers will spend more than \( 367.2600 \) is \( P(\sum x > 367.2600) = 0.2357 \).

\(\boxed{0.2357}\)

Is the assumption of normal necessary?

Assumption of normality

The assumption of normality is necessary for the calculations made in this context.

\(\boxed{\text{Yes}}\)

The owner of Don Mcalds gives a coupon for a free sundae to the 4, at least how much must a group of 50 spend in total to get the free sundae?

Minimum total spending calculation

The minimum amount a group of 50 must spend to get a free sundae is \( 375.5888 \).

\(\boxed{375.5888}\)

The distribution of \( X \) is \( \boxed{X \sim N(7.17, 1.72)} \).

The distribution of \( \sum x \) is \( \boxed{\sum x \sim N(358.5, 12.1622)} \).

The probability that one randomly selected customer will spend more than \( 7.3552 \) is \( \boxed{0.4571} \).

The probability that the average spent by 50 customers is less than \( 7.3452 \) is \( \boxed{0.7643} \).

The probability that the 50 customers will spend more than \( 367.2600 \) is \( \boxed{0.2357} \).

The assumption of normality is necessary, \( \boxed{\text{Yes}} \).

The minimum amount a group of 50 must spend to get a free sundae is \( \boxed{375.5888} \).

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