Of all customers purchasing automatic garage-door openers, 75% purchase Swedish model. Let X = the number among the next 15 purchasers who select the Swedish model.
(a) What is the pmf of X?
(b) Compute P(X > 10).
(c) Compute P(6 ≤ X ≤ 10).
(d) Compute μ and σ2.

a)

For any integer k between 0 and 15, and 0 for other values of k.

b)

c) P(6 ≤ X ≤ 10) = 0.2737

d)  μ = 15*0.75 = 11.25. σ² = 11.25*0.25 = 2.8125

Step-by-step explanation:

X is a binomial random variable with parameters n = 15, p = 0.75. Therefore

a)

For any integer k between 0 and 15, and 0 for other values of k.

b)

P(X>10) = P(X=11) + P(X=12)+ P(X=13)+P(X=14)+P(x=15)

Thus,

c) P(6 ≤ X ≤ 10) = P(X = 6) + P(X = 7) + P(X = 8) + P(X=9) + P(X=10)

Thereofre,

d)  μ = n*p =  15*0.75 = 11.25

σ² = np(1-p) = 11.25*0.25 = 2.8125

12

step-by-step explanation: