Question

The amount of calories consumed by customers at the Chinese buffet is normally distributed with mean 2833 and standard deviation 663. 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 2436 calories.  

c. What proportion of the customers consume over 3123 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

a)

X ~ N(2833,663)

b)

µ =    2833              
σ =    663              
left tailed                  
P( X < 2436.000   )          
                  
Z =(X - µ ) / σ = (   2436   -   2833   ) /    663
Z =    -0.599              
P(X < 2436   ) = P(Z < -0.60   ) =   0.2747

excel formula for probability from z score is =NORMSDIST(Z)

c)

µ =    2833                          
σ =    663                          
right tailed                              
P ( X ≥   3123   )                      
                              
Z =   (X - µ ) / σ = (   3123.00   -   2833   ) /    663   =   0.437
                              
P(X ≥   3123   ) = P(Z ≥   0.437   ) =   P ( Z <   -0.437   ) =    0.3309

d)

µ=   2833                  
σ =    663                  
top 2% =bottom 98% or 0.98                  
                      
Z value at    0.98   =   2.0537 (excel formula =NORMSINV(   0.98   ) )
z=(x-µ)/σ                      
so, X=zσ+µ=   2.054   *   663   +   2833  
X   =   4194.636              

answer: 4195