Question

You were told that the mean score on a statistics exam is 75 with the scores normally distributed. In addition, you know the probability of a score between 55 and 60 is 4.41% and that the probability of a score greater than 90 is 6.68%. What is the probability of a score between 55 and 95?

Answer 1

From the given information we have –

Pr (x > 90) = 0.0668,

Pr (z > z1 ) = 0.0668

Pr ( z < z1) = 1 - Pr (z > z1 )

= 1.0 - 0.0668 = 0.9332

From the standard normal table , the 0.9332 Probability is at z = 1.50.

Therefore    z = (x – mean) / sd

1.5 = (90 – 75) / sd

1.5 = 15 / sd

Sd = 10    

μ=75, σ=10

We need to compute Pr(55≤X≤95). The corresponding z-values needed to be computed are:

Therefore, we get:

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