Question

A tire manufacturer knows that 5% of tires contain a defect, and the presence of a defect is independent from tire to tire.

Answer 1

The probability that if 5 tires are inspected, exactly 2 have a defect is 0.021

How to calculate the probability

The given parameters are:

$p = 5\%$ --- the proportion that contains defect

$n =5$ --- the sample size

$r =2$ -- the selected sample

The probability is then calculated as:

$P(x =r) = ^nC_r * p^r * (1 - p)^{n-r}$

So, we have:

$P(x =2) = ^5C_2 * (5\%)^2 * (1 - 5\%)^{5-2}$

$P(x =2) = 10 * (5\%)^2 * (1 - 5\%)^3$

$P(x =2) = 0.021$

Hence, the probability that if 5 tires are inspected, exactly 2 have a defect is 0.021

Read more about probabilities at:

brainly.com/question/15246027

Answer 2

N=5

K=2

P=0.05

CoE= 10

10 x (0.05)^2 x (0.95)^3

10 x (0.0025) x (0.8573) = 0.0214

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