Question

The amount of calories consumed by customers at the Chinese buffet is normally distributed with mean 2932 and standard deviation 585. One randomly selected customer is observed to see how many calories X that customer consumes. Round all answers to 4 decimal places where possible.

a. What is the distribution of X? X ~ N(,)

b. Find the probability that the customer consumes less than 2644 calories.

c. What proportion of the customers consume over 3200 calories?

d. The Piggy award will given out to the 2% of customers who consume the most calories. What is the fewest number of calories a person must consume to receive the Piggy award?  calories. (Round to the nearest calorie)

Answer 1

Let X denote the amount of calories consumed by customers at the Chinese buffet .

a)

b)

i.e.

Now,

                    

c)

                           

Proportion of the customers consume over 3200 calories = 32.28%

d)

Let c be the required number of calories a person must consume to receive the Piggy award.

It is given that,

The fewest number of calories a person must consume to receive the Piggy award is 4137.

z table :