SOLUTION: The amount of calories consumed by customers at the Chinese buffet is normally distributed with mean 2928 and standard deviation 571. One randomly selected customer is observed to

Question 1169017: The amount of calories consumed by customers at the Chinese buffet is normally distributed with mean 2928 and standard deviation 571. 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?
b. Find the probability that the customer consumes less than 2772 calories.
c. What proportion of the customers consume over 3124 calories?
d. The Piggy award will given out to the 1% 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 by Boreal(15235) (Show Source): You can put this solution on YOUR website!
it is normally distributed with mean 2928 cal and sd 571 cal (variance 571^2 cal^2)
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z=(x-mean)/sd
z< (2772-2928)/571 or -156/571 or -0.27
this probability is 0.3923
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z>(3124-2928) or 196/571 or 0.34
that probability is 0.3657
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can check those by using normalcdf (2772,3124,2928,571) ENTER and get probability 0.2419.
That is the probability between the two, and the three probabilities should add to 1, which given rounding error, do.
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The 99%ile is 2.326
so 2.326=(x-2928)/571
1328.3=x-2928
x=4256 cal
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