Question

5.28 A manufacturer knows that on average 20% of the electric toasters produced require repairs within 1 year after they are sold. When 20 toasters are randomly selected, find appropriate numbers x and y such that (a) the probability that at least x of them will require repairs is less than 0.5; (b) the probability that at least y of thE?

Answer 1

A) probability that at least x of them will require repairs is less than 0.5 is 4

Explanation:

sample size, n = 20

p = success probability of toaster = 0.2

q = failure probability of toaster =1- p = 1- 0.2 =0.8

mean, , μ = n * p = 20 * 0.2 = 4

standard deviation,
`\sigma = √(npq) = √((20 * 0.2 *0.8)) = 1.79`

a) the probability that at least some of them require repairs < 0.5.

for
`p \geq 0.5` value of z = 0

we know
`z  =(x -\mu)/(\sigma)`

`0 = (X -4)/(1.79)` from z table

X = 4

B) SECOND PART IS INCOMPLETE { DATA IS INCOMPLETE}