Historically, 65% of customers who have entered a store have made a purchase (ea

Question

Historically, 65% of customers who have entered a store have made a purchase (each customer can make only a single purchase). The average purchase for these customers is $205.00. If on a particular day, 512 customers visit a store, calculate the following (assuming that each customer is equally likely to make a purchase):

a. Probability that more than 315 customers will make a purchase

b. Probability than no more than 310 customers will make a purchase

c. Probability that between 320 (inclusive) and 325 (inclusive) purchases will be made.

d. What is the probability that EXACTLY 305 customers will make a purchase?

Explanation / Answer

This is the Binomail Distribution with n = 512 and p = 0.65

a) P(X>315)

Use Excel function

1-BINOM.DIST(315,512,0.65,TRUE) = 0.9448

So, answer is 0.9543

b) P(X<=310)

Use Excel function

BINOM.DIST(310,512,0.65,TRUE) = 0.0201

So, answer is 0.0201

c) P(320<=X<=325)

Use excel function

BINOM.DIST(325,512,0.65,TRUE)-BINOM.DIST(319,512,0.65,TRUE)

= 0.1393

d) P(X = 305)

Use excel function

BINOM.DIST(305,512,0.65,FALSE)

= 0.0014

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