Question

The average amount of money that people spend at Don Mcalds fast food place is $7.7000 with a standard deviation of $1.8900. 46 customers are randomly selected. Please answer the following questions, and round all answers to 4 decimal places where possible and assume a normal distribution.

1. What is the distribution of XX? XX ~ N(,)
2. What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
3. What is the distribution of ∑x∑x? ∑x∑x ~ N(,)
4. What is the probability that one randomly selected customer will spend less than $7.9120?
5. For the 46 customers, find the probability that their average spent is more than $7.9120.
6. Find the probability that the randomly selected 46 customers will spend more than $363.9520.
7. For part e) and f), is the assumption of normal necessary? YesNo
8. The owner of Don Mcalds gives a coupon for a free sundae to the 5% of all groups of 46 people who spend the most money. At least how much must a group of 46 spend in total to get the free sundae? $

Answer 1

a. The distribution of X is ,

b. The distribution of is ,

Where ,

c. The distribution of is ,

where ,

d. Now ,

; From standard normal distribution table

Therefore , probability that one randomly selected customer will spend less than $7.9120 is 0.5438