The weights of oven-stuffer roaster chickens have approximately a normal distribution with= 6.1 pounds and a standard deviation of= 0.7 pounds. Suppose that we randomly select n = 81 oven-stuffer roaster chickenss and measure their weights in pounds. LetXbe the random variable representing the mean weight of the selected chickens. Let Xtot be the random variable representing the total weight of the selected chickens.

a) About what proportion of oven-stuffer roaster chickens have weights between 6 and 7 pounds?

b) About what proportion of oven-stuffer roaster chickens have weights greater than 7 pounds?

c) About how many of the 81 sampled chickens have weights less than 6.5 pounds? (nearest integer)

d) d. About how many of the sampled chickens have weights between 6 and 7 pounds? (nearest integer)

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

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

g) What is the probability that 6 <X< 6.2?

h) What is the probability that Xtot > 500?

f) Copy your R script for the above into the text box here.