Question

7.19 a normal distribution has the mean 74.4 find its standard deviation if 10% of the area under the curve lies to the right of 100

Answer 1

Solution :

mean = $\mu$ = 74.4

standard deviation = $\sigma$ = ?

X = 100

Using standard normal table,

P(Z > z) = 10%

1 - P(Z < z) = 0.10

P(Z < z) = 1 - 0.10 = 0.90

P(Z < 1.28) = 0.90

z = 1.28

Using z-score formula,

x = z * $\sigma$ + $\mu$

$\sigma$ = (x - $\mu$) / z = (100 - 74.4) / 1.28 = 20

Standard deviation = 20