Question

The length of time needed to complete a certain test is normally distributed with mean 92 minutes and standard deviation 8 minutes. Find the probability that it will take less than 80 minutes to complete the test.

Answer 1

The probability that it will take less than 80 minutes

P(X≤80) = 0.0768

Explanation:

Step(i):-

Given mean of the Population = 92 minutes

Given standard deviation of the Population = 8 minutes

Let 'X' be the random variable in normal distribution

Let 'X' = 80 minutes

`Z = (x-mean)/(S.D) = (80 - 92)/(8) = -1.5`

Step(ii):-

The probability that it will take less than 80 minutes

P(X≤80) = P(Z≤-1.5)

= 0.5 - A(1.5)

= 0.5 - 0.4232

=0.0768

Final answer:-

The probability that it will take less than 80 minutes

P(X≤80) = 0.0768