Question

A manufacturer knows that, on average, 7.5% of the electric toasters that he makes will require repairs within 90 days after they are sold. Determine the probability that among 100 of these toasters.

(a) at least 5 will require repairs within the first 90 days after they are sold.

(b) between 5 and 8, exclusive, will require repairs within the first 90 days after they are sold.   

Answer 1

Solution:-

n = 100,

p = 0.075

a) The probability that at least 5 will require within the first 90 days after they are sold is 0.8777.

x = 5

By applying binomial distribution:-

P(x > 5) = 0.8777

b) The probability that between 5 and 8 exclusive will require within the first 90 days after they are sold is 0.2910

x₁ = 5

x₂ = 8

By applying binomial distribution:-

P(5 < x < 8) = P(x = 6) + P(x = 7)

P(5 < x < 8) = 0.1393 + 0.1517

P(5 < x < 8) = 0.2910