Question

7 points

A manufacturer of laptops finds that on the
average, 0.2 of his products are rejected
because they contain some technical
problems. If we take a sample of 11
laptops
:- What's the probability that the sample
will contain less than three rejects?
What's the probability that the sample
will contain at least three rejects?
How many rejects do you expect that
the sample will contain ?

Answer 1

Explanation:

Let x be a random variable representing the products are rejected

because they contain some technical

problems. This is a binomial distribution since the outcomes are two ways. It is either they are rejected or accepted. The probability of success(that they would be rejected), p = 0.2

The probability of failure, q would be 1 - p = 1 - 0.2 = 0.8

n = 11

a) We want to determine P(x < 3)

From the binomial distribution table,

P(x < 3) = 0.62

b) We want to determine P(x ≥ 3)

From the binomial distribution table,

P(x ≥ 3) = 0.38

c) The number of rejects that the sample is expected to contain is the mean.

mean = np

mean = 11 × 0.2 = 2.2

Approximately 2 rejects