Question

A Jersey Mike’s franchise specifies that the average (mean) amount of meat on a regular-sized Italian sub should be 8 ounces and the standard deviation only 0.5 ounces. A secret shopper picks out a sub at random in one of the franchises and finds that it is made with 6.9 ounces of meat. Assume that the amount of meat on a sub follows a normal distribution. If the amount of meat is below the mean by more than 3 standard deviations, the owner may get a scathing Yelp review. How many standard deviations from the mean is 6.9?

A. -2.20

B. -1.10

C. 2.20

D. 1.10

Answer 1

Solution:
Given in the question
Population mean () = 8
Population standard deviation () = 0.5
the amount of meat on a sub follows a normal distribution, We need to calculate how many standard deviations from the mean is 6.9 which can be shown as Z-score, Z-score can be calculated as
Z-score = (X - )/ = (6.9-8)/0.5 = -1.1/0.5 = -2.20
So its correct answer is A. i.e. -2.20, so we can say that X=6.9 is 2.20 standard deviation below from the mean.