Question

The amount of calories consumed by customers at the Chinese buffet is normally distributed with mean 2651 and standard deviation 599. One randomly selected customer is observed to see how many calories X that customer consumes. Round all answers to 4 decimal places where possible, unless otherwise specified. a. What is the distribution of X? X-N b. Find the probability that the customer consumes less than 2548 calories. c. What proportion of the customers consume over 2861 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

cal Aus lef x be the amount of calones consumed by customers at the Chinese buffet Criven that Xy N (4,02) with u = 2651 and o2599 30 that 2=XY UN0,1) The distribution of x is N (M=2651, 0= 599) (6) The prob that a customes consumes less than 2548 calories is PIX < 2548) = P12<2598-2051 )=P(Z<-011719) = 1- (0.1719) = 1-0.5682= 0.4318 (c) The proportion of the customers consuming over 286 1 calories is Plz>0.3506) 599 = 1-P170,3506)= 1-0 (0.3506)= 1-0.637150.3629 (d) The piggy award will be given to the 2% of eas customers who consume the most calosies. That id PCXZN = 0,02 I P(XCX) = 0.98 P(2<2-4)=0.98 = (2.054) 0139 $(x, ) = $(2.054) =) P-4 = 2.054 >> 2= 4 + 2,0540 = 3881.346 So the sewest number of calories a person must consume to receive piggy qwand is 3881 calories P(X72061)= Plz> 2061- 2651 21) = !