The manager of a supermarket found that 72 of the shoppers w

The manager of a supermarket found that 72% of the shoppers who taste a free sample of a food item will buy the item. Assume that 50 randomly selected shoppers taste a free sample of food. a) state the random variable. b) argue that this is a binomial experiment. c) find the mean number of shoppers who will buy the item. d) find the standard deviation for the number of shoppers who will buy the item. e) find the probability that exactly 25 will buy the food item. f) find the probability that at most 13 shoppers will buy the food item. g) find the probability that at least 29 shoppers will buy the food item. h) without drawing a histogram, decribe the shape of the histogram. i) if at most 13 shoppers did buy the item, what might that tell you?

Solution

a) random variable would be {0,1,2,......50}

b) it is a binomial experiment as there can be two results either the people who taste will buy or not buy

c) (.72)*0 + (.72)*1..................(.72)*50 approx

d)?² = ? { [ x_i - E(x) ]² * P(x_i) } xi = 0 to 50 P(xi) = .72

e) (.72)^25 * (.28)^25

f)  ? 50Cr (.72)^ r * (.28)^(50-r) r = 0 to 13

g)1 - ? 50Cr (.72)^ r * (.28)^(50-r) r = 0 to 28

h) parabola