Question

A hamburger franchise specifies that the average serving size for an order of large fries should be 168 grams and the standard deviation only 2.5 grams. If the serving is below the mean by more than 3 standard deviations, the restaurant will be in danger of losing its franchise. A franchise inspector picks out an order of large fries at random from both the City Burger Joint and the Country Burger Joint. His two random samples shows a serving size for the large fries at the City Burger Joint is 160 grams and 174 grams at the Country Burger Joint. (Assume that the serving size for a large fry is normally distributed).

1. What does a negative z-score represent in the context of this problem? (.5 pt.)

2. What does a positive z-score represent in the context of this problem? (.5 pt.)

3. What is the serving size of a large fry that corresponds to a standard score of z = 2.5? Show your work.(1 pt.)

4. does an order of large fries contain 174.25 grams of fries occur very often? Explain why. (1 pt.)

Answer 1

(a) A negative z value means that the corresponding value of variable is below the mean value. In the context of this problem, negative value of z means the serving size of large fries is below or less than the average size.

(b) A positive z value means that the corresponding value of variable is above the mean value. In the context of this problem, positive value of z means the serving size of large fries is above or greater than the average size.

(b) we have

we have to find the x value corresponding to a z value of 2.5

Using the formula

setting the given values, we get

2.5 = (x-168)/2.5

this gives

2.5*2.5 = x-168

or x-168 = 6.25

and x = 174.25

So, serving size is 174.25g

(d) No, because 174.25 is more than 2 standard deviation away from the mean, which means there is very low chances of finding a serving size of 174.25 g. We know that 95% of the data fall within 2 standard deviation of the mean, so 174.25g is outside the 95% values, it is not occurring often.