Question

THE RESULTS OF A SATISTICS EXAMINATION ARE NORMALLY DISTRIBUTED WITH A MEAN OF 74 AND A STANDARD DEVIATION OF 8 FIND THE % OF INDIVIDUALS THAT SCORED LESS THEN A 78

Answer 1

Given

Mean = 74

standard deviation = 8

Find

percent of individuals that scored less than a 78

Explanation

as we have given ,

mean = 74

standard deviation = 8

P(X < 78) =

$\begin{gathered} P(Z<\frac{X-\mu}{\sigma}) \\ =P(Z<\frac{78-74}{8}) \\ =P(Z<\frac{4}{8}) \\ =P(Z<0.5) \\ =0.6915\approx69.15\% \end{gathered}$

Final Answer

Hence , the percentage of individuals that scored less than 78 is 69.15% or 69.2%