The time it takes to install the new telephone is found to be normally distributed with the mean of x minutes and a standard deviation of 8 minutes. If the probability of installing a new telephone more than 65 minutes is 0.0062, find the value of x.

Answer 1

To solve this problem, we need to find the z-score corresponding to the probability of installing a new telephone more than 65 minutes.

First, we calculate the z-score using the formula:

z = (x - μ) / σ

where x is the value, μ is the mean, and σ is the standard deviation.

In this case, x = 65, σ = 8, and we want to find the value of μ.

To find the z-score, we rearrange the formula:

z = (x - μ) / σ
z = (65 - μ) / 8

Next, we look up the z-score in the standard normal distribution table to find the corresponding probability.

Using the table, we find that the z-score corresponding to a probability of 0.0062 is approximately -2.72.

Therefore, we can set up the equation:

-2.72 = (65 - μ) / 8

Now, we can solve for μ:

-2.72 * 8 = 65 - μ
-21.76 = 65 - μ
μ = 65 - (-21.76)
μ = 65 + 21.76
μ = 86.76

Therefore, the value of x (the mean time it takes to install a new telephone) is 86.76 minutes.