Question

A manufacturer of Christmas light bulbs knows that 10% of these bulbs are defective. It is known that light bulbs are defective independently. A box of 150 bulbs is selected at random. Answer the following questions.

Please show the work inputed onto calculator thank you!

Answer 1

2)

Let X denote the number of light bulbs in the sample that a defective.

Then

X - Bin(n = 150, p = 0.10)

1150 P(X = z) = (0.10)"(1 – 0.10) 150-1, 1 = 0, 1, 2, ... 150

Required probability =

P(X < 20) = P(X = 0) + P(X = 1) + ... + P(X = 20)

(150)。 (0.10) (1-0.10) 150-0 + 09279 (150 + ( (0.10521- 0.10 150-20

3)

Here,

X - Bin(n = 150, p = 0.10)

So, E(X) = np = 150(0.10) = 15

4)

Here,

X - Bin(n = 150, p = 0.10)

So,

Std. Dev(X) = np(1 - p) = 150(0.10)(1 – 0.10) = 3.67