3. Binomial Random Variable: On your way home from work at 9pm every day, you pa

Question

3. Binomial Random Variable: On your way home from work at 9pm every day, you pass your favorite pizza store. You estimate that 25% of the time, they have at least one slice of pepperoni pizza (your favorite) remaining, 75% of the time, they have already sold out of slices. Assume that whenever there is pizza available, you will buy one slice. Consider the last 10 days and let X represent the number of pizza slices you purchased on the way home from work. a. For this experiment, define the event that represents a "success" b. Explain why X is (approximately) a binomial random variable. c. Give the value of p for this binomial experiment. d. Find P(Xo). g. How many slices of pepperoni pizza do you expect to purchase over a time period of 10 days?

Explanation / Answer

a) Success is the event that they have at least one slice of pepperoni pizza remaining.

b) X is binomial distribution because each day is independent of other day. Meaning chance of availablity of pizza is same for all 10 days

c) p = 0.25

d) P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

                   = 10C0 * 0.250 * 0.7510 + 10C1 * 0.251 * 0.759 + 10C2 * 0.252 * 0.758 + 10C3 * 0.253 * 0.757 + 10C0 * 0.254 * 0.756

                   = 0.9219

e) P(X = 3) = 10C3 * 0.253 * 0.757 = 0.2503

f) P(X > 0) = 1 - P(X = 0) = 1 - 10C0 * 0.250 * 0.7510 = 1 - 0.0563 = 0.9437

g) Expected value = n * p = 10 * 0.25 = 2.5 or 3 (approximately)

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