Question

1. Given that a random variable, x, is normally distributed with mean 10 and standard deviation 3, find:
   1. The z score with area 0.3 to the right of z.
   2. The associated x value with the z score of part a).

Answer 1

solution

Given that,

mean = = 10

standard deviation = =3

Using standard normal table,

P(Z > z) = 0.3

= 1 - P(Z < z) = 0.3

= P(Z < z ) = 1 - 0.3

= P(Z < z ) = 0.7

z = 0.52 (using standard normal (Z) table )

b.

Using z-score formula  

x = z * +

x= 0.52 *3+10

x= 11.56