On a test with a population mean of 75 and standard deviation equal to 16, if the scores are normally distributed, what percentage of scores fall between 70 and 80?

Percentage of scores that fall between 70 and 80 = 24.34%

Step-by-step explanation:

We are given a test with a population mean of 75 and standard deviation equal to 16.

Let X = Percentage of scores

Since, X ~ N()

The z probability is given by;

           Z = ~ N(0,1)    where, = 75  and   = 16

So, P(70 < X < 80) = P(X < 80) - P(X <= 70)

P(X < 80) = P( < ) = P(Z < 0.31) = 0.62172

P(X <= 70) = P( < ) = P(Z < -0.31) = 1 - P(Z <= 0.31)

                                              = 1 - 0.62172 = 0.37828

Therefore, P(70 < X < 80) = 0.62172 - 0.37828 = 0.24344 or 24.34%