Question

The average amount of money that people spend at Don Mcalds fast food place is $7.5600 with a standard deviation of $1.5100. 14 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. For the 14 customers, find the probability that their average spent is more than $8.0946.
2. Find the probability that the randomly selected 14 customers will spend more than $113.3244.
3. For part e) and f), is the assumption of normal necessary? YesNo
4. The owner of Don Mcalds gives a coupon for a free sundae to the 2% of all groups of 14 people who spend the most money. At least how much must a group of 14 spend in total to get the free sundae? $

Answer 1

a) Let x denote the amount spend by a customer

X follows normal distribution with mean 7.56 and standard deviation 1.51

To find

As X follows normal distribution also has normal distribution with mean 7.56 and standard deviation 0.40356 (standard deviation/n^0.5).

Therofore converting to standard normal

  

This is the required probability

B)To find

We know that X follows normal Sum X will follow normal with mean 14*7.51=105.14 and standard deviation (14^0.5)*1.51=5.6499

Converting above probability to standard normal

Hence this is required probability

c) part e and f is not given hence nothing can be said about it.

d) Let D be the amount a group of 14 has to spend to get the coupon that is to find D such that

Again converting to standard normal

Therfore

Therfore

Hence a group of 14 has to spend minimum of 116.7222$.