Question

Of all customers purchasing automatic garage-door openers, 75% purchase a chain-driven model. Let X = the number among the next 15 purchasers who select the chain-driven model.

(a) What is the pmf of X?

a) h(x; 3, 15, 75)

b) nb(x; 15, 0.25)

c) b(x; 15, 0.25)

d) h(x; 12, 15, 75)

e) nb(x; 15, 0.75)

f) b(x; 15, 0.75)

(b)

Compute P(X > 10).(Round your answer to three decimal places.)

P(X > 10) =

(c) ComputeP(7 ≤ X ≤ 10).(Round your answer to three decimal places.)

P(7 ≤ X ≤ 10) =

(d) Compute μ and σ².μ = σ² =

(e)If the store currently has in stock 10 chain-driven models and 5 shaft-driven models, what is the probability that the requests of these 15 customers can all be met from existing stock? (Round your answer to three decimal places.)

Answer 1

Answer: Of all customers purchasing automatic garage-door openers, 75% purchase a chain-driven model. Let X = the number among the next 15 purchasers who select the chain-driven model.

Solution:

n = 15

p = 75% = 0.75

(a) What is the pmf of X?

The option f. is correct answer.

b(x; 15, 0.75)

Therefore,

a) b(x; 15, 0.75)

b) P(X > 10) = 0.686

c) P(7 ≤ X ≤ 10) = 0.309

d) μ = 11.25

σ2 = 2.8125

e) 0.852