1. Suppose that we are analyzing the purchase decision of the next 3 customers e

Question

1. Suppose that we are analyzing the purchase decision of the next 3 customers entering a clothing store. On the basis of past experience, the store manager estimates that the probability that any one customer will make a purchase (i.e., the probability of success) is .25. What is the probability that one of the next three customers will make a purchase?

(a) 0.6578

(b) 0.3321

(c) 0.2258

(d) 0.4219

(e) None of the above.

2. The assembly time for a product is uniformly distributed between 6 to 10 minutes. What is the probability of assembling the product between 6 to 8.5 minutes?

(a) 0.6250

(b) 0.2550

(c) 0.8590

(d) 0.7550

(e) None of the above.

Explanation / Answer

1)

X ~ Binomial (n,p)

Where n = 3 , p = 0.25

Binomial probability distribution is

P(X) = nCx px (1-p)n-x

So,

P( X = 1) = 3C1 0.251 0.752

= 0.4219

2)

X ~ Uniform (a,b)

Where a = 6 , b = 10

We have to calculate P( 6 <= X <= 8.5) = ?

For Uniform distribution,

P(c <= X <= d) = ( d - c) / ( b - a)

Therefore,

P( 6 <= X <= 8.5) = (8.5 - 6) / (10 - 6)

= 0.6250

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