Question

The average amount of money that people spend at Don Mcalds fast food place is $7.2000 with a standard deviation of $1.5000. 15 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 $6.7891?
5. For the 15 customers, find the probability that their average spent is more than $6.7891.
6. Find the probability that the randomly selected 15 customers will spend more than $101.8365.
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 2% of all groups of 15 people who spend the most money. At least how much must a group of 15 spend in total to get the free sundae? $

Answer 1

a)X ~N(7.2,1.5)

b)

std error=σx̅=σ/√n=

0.3873

x-~ N(7.2, 0.3873)

c)

∑x~ N(108 , 5.8095)

d)

probability =P(X<6.7891)=(Z<6.7891-7.2)/1.5)=P(Z<(-0.2739)=0.3921

e)

probability =P(X>6.7891)=P(Z>(6.7891-7.2)/0.387)=P(Z>-1.06)=1-P(Z<-1.06)=1-0.1444=0.8556

f)

probability =P(X>101.8365)=P(Z>(101.8365-108)/5.809)=P(Z>-1.06)=1-P(Z<-1.06)=1-0.1444=0.8556

g) yes (Since sample size <30)

h)

for 98th percentile critical value of z=		2.054
therefore corresponding value=mean+z*std deviation=			119.9312