Assume that customers come into a store to either make a purchase or first. The

Question

Assume that customers come into a store to either make a purchase or first. The retailer tracked 50 customers. It had been historically calculated that the proportion that bought was approximately 30% (0.3). This is the outcome of interest. Assume that you can life the Binomial approximation to the Normal distribution. Please consider continuity corrections. Given this information: a.) To pay a bonus, at least 20 customers should make a purchase. What is the probability that a bonus is paid out given 50 customers visiting the retailer?

Explanation / Answer

a).

n=50

p=0.3

Expectation = np = 15

Variance = np(1 - p) = 10.5

Standard deviation = 3.2404

P( x at least 20 custemers)

With continuity correction, z value for 20,

Z=(19.5-15)/3.2404 =1.26

P( x 20) =P( z >1.26)

= 0.1038

b).

P( no more than 5 )

With continuity correction, z value for 5,

Z=(5.5-15)/3.2404 =-2.93

P( x 5) =P( z < -2.93)

= 0.0017

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