## 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

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## Answers ( )

Answer: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%