Question

A part manufactured by plastic injection molding has a historical mean of 100 and a historical standard deviation of 8. Find the value of the mean thickness required to make the probability of exceeding 101 less than 8%.

Answer 1

The probability of thickness exceeding 101 is 0.4483.

Explanation:

Let X denote the thickness of the part manufactured by plastic injection molding.

Assume that X follows a normal distribution with mean, μ = 100 and standard deviation, σ = 8.

Compute the probability of thickness exceeding 101 as follows:

`P(X>101)=P((X-\mu)/(\sigma)>(101-100)/(8))`

`=P(Z>0.125)\\\\=1-P(Z<0.125)\\\\=1-0.55172\\\\=0.44828\\\\\approx 0.4483`

Thus, the probability of thickness exceeding 101 is 0.4483.