Question

A company makes rubber rafts. 12% of them develop cracks within the first month of operation. 27 new rafts are randomly sampled and tested, by being used for one month, under standardized conditions that mimic typical operating conditions. Calculate the probability that the number of tested rafts that develop cracks is no more than 3. Round your answer to four decimal places.

Answer 1

The probability that the number of tested rafts that develop cracks is no more than 3 is .00006.

The true proportion, p for the population is given to 0.12.

Thus, the mean, μ, for the sample = np = 27*0.12 = 3.24.

The sample size, n, given to us is 27.

Thus, the standard deviation, s, for the sample can be calculated using the formula, s = √{p(1 - p)}/n.

s = √{0.12(1 - 0.12)}/27 = √0.003911 = 0.0625389.

We are asked to calculate the probability that the number of tested rafts that develop cracks is no more than 3, that is, we need to calculate P(X ≤3).

P(X ≤ 3)

= P(Z ≤ {(3 - 3.24)/0.0625389) {Using the formula z = (x - μ)/s}

= P(Z ≤ -3.8376114706)

= .00006 {From table}.

Thus, the probability that the number of tested rafts that develop cracks is no more than 3 is .00006.

Learn more about sampling distributions at

brainly.com/question/15507495

#SPJ4