Question

One of the Hamburgers sold at Citi Field is advertised as containing 530 calories. In actuality the number of calories in the Hamburgers sold has approximately a normal distribution with μ= 538 calories and a standard deviation of σ= 7.6 calories. Suppose that we randomly select 144 Citi Field hamburgers. Let X be the random variable representing the mean number of calories and let Xtot be the random variable representing the sum of the calories in the 144 selected hamburgers.

a) About what proportion of Citi Field hamburgers have between 530 and 540 calories?  

b) About proportion of Citi Field hamburgers have more than 543 calories?  

c) About how many of the 144 sampled hamburgers have less than 530 calories? (nearest integer)  

d) About how many of the 144 sampled hamburgers have between 540 and 550 calories in them? (nearest integer)  

e) What is the standard deviation of the distribution of X?  

f) What is the standard deviation of the distribution of Xtot?  

g) What is the probability that 537 < X < 539?  

h) What is the probability that Xtot > 77600?  

Answer 1