manufacurer is developing a new type of paint based on the results of the test the manufacturer concluded that the mean life efore corrosive failure for the nrew paint is 155 hours with a standard deviation find probability that paint on a sample of 65 test panels will have mean life before corrosive failure of less that

The probability is 0.0005.

Explanation:

The stated question is incomplete. The complete question is as follows.

A manufacturer is developing a new type of paint. Test panels were exposed to various corrosive conditions to measure the protective ability of the paint. Based on the results of the test, the manufacturer has concluded that the mean life before corrosive failure for the new paint is 155 hours with a standard deviation of 27 hours. If the manufacturer's conclusions are correct, find the probability that the paint on a sample of 65 test panels will have a mean life before corrosive failure of less than 144 hours.

The mean life is 155 hours. Hence, μ = 155.

The standard deviation is 27 hours. Hence, σ = 27.

The sample size in 65 test panels. Hence, n = 65.

We can use the central limit theorem to find the probability that the mean life before corrosive failure is less than 144 hours. By the central limit theorem:

P (X < 144) = P[ (X - μ) / (σ / √n) < (144 - 155) / (27/√65) ]

P (X < 144) = P (Z < - 3.2846)

Using the Z-value table for normal distribution, this value turns out to be:

P (X < 144) = 0.0005