Question

The average amount of money that people spend at Don Mcalds fast food place is $7.9500 with a standard deviation of $1.8200. 43 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 X? X ~ N(,) _____
2. What is the distribution of ¯x? ¯x ~ N(,) _____
3. What is the distribution of ∑x? ∑x ~ N(,) _____
4. What is the probability that one randomly selected customer will spend more than $7.9938?  _____
5. For the 43 customers, find the probability that their average spent is less than $7.9938.  _____
6. Find the probability that the randomly selected 43 customers will spend more than $343.7334.  _____
7. For part e) and f), is the assumption of normal necessary? Yes or No
8. The owner of Don Mcalds gives a coupon for a free sundae to the 4% of all groups of 43 people who spend the most money. At least how much must a group of 43 spend in total to get the free sundae? $_____

Answer 1

Given:

= 7.9500, = 1.8200, n = 43

a)

X ~ N(x, x)

X ~ N( 7.9500, 1.8200)

b)

~ N (x, x/ )

~ N( 7.9500, 1.8200/)

~ N (7.9500, 0.2775)

C)

D)

Find: P(X > 7.9938)

             .....................Using standard Normal table