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

Answer:

The probability of thickness exceeding 101 is 0.4483.

Step-by-step 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:

$P(X>101)=P(\frac{X-\mu}{\sigma}>\frac{101-100}{8})$

                    $=P(Z>0.125)\\\\=1-P(Z$

Thus, the probability of thickness exceeding 101 is 0.4483.