Question

Suppose x is a normally distributed random variable with μ=33 and σ=4

Find a value x0 of the random variable x that satisfies the following equations or statements.

a. 10% of the values of x are less than x0.

b. 1% of the values of x are greater than x0.

Answer 1

Solution:-

Given that,

mean = = 33

standard deviation = = 4

a) Using standard normal table,

P(Z < z) = 10%

= P(Z < z ) = 0.10

= P(Z < -1.28 ) = 0.10  

z = -1.28

Using z-score formula,

x0 = z * +

x0 = -1.28 * 4 + 33

x0 = 27.88

b) Using standard normal table,

P(Z > z) = 1%

= 1 - P(Z < z) = 0.01  

= P(Z < z) = 1 - 0.01

= P(Z < z ) = 0.99

= P(Z < 2.33 ) = 0.99  

z = 2.33

Using z-score formula,

x0 = z * +

x0 = 2.33 * 4 + 33

x0 = 42.32