The length of time needed to complete a certain test is normally distributed with mean 35 minutes and standard deviation 15 minutes. Find the probability that it will take between 31 and 40 minutes to complete the test.

Probability = 0.23572 .

Step-by-step explanation:

We are given that the length of time needed to complete a certain test is normally distributed with mean 35 minutes and standard deviation 15 minutes.

Let X = length of time needed to complete a certain test

Since, X ~ N()

The z probability is given by;

            Z = ~ N(0,1)    where, = 35  and   = 15

So, P(31 < X < 40) = P(X < 40) - P(X <= 31)

P(X < 40) = P( < ) = P(Z < 0.33) = 0.62930

P(X <= 31) = P( < ) = P(Z < -0.27) = 1 - P(Z <= 0.27)

                                               = 1 - 0.60642 = 0.39358

Therefore, P(31 < X < 40) = 0.62930 - 0.39358 = 0.23572 .  

answer

false

explanation

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