Question

The random variable X is normally distributed. Also, it is known that P(X > 161) = 0.04. [You may find it useful to reference the z table.]

a. Find the population mean μ if the population standard deviation σ = 13. (Round "z" value to 3 decimal places and final answer to 2 decimal places.)

b. Find the population mean μ if the population standard deviation σ = 24. (Round "z" value to 3 decimal places and final answer to 2 decimal places.)

c. Find the population standard deviation σ if the population mean μ = 139. (Round "z" value to 3 decimal places and final answer to 2 decimal places.)

d. Find the population standard deviation σ if the population mean μ = 122. (Round "z" value to 3 decimal places and final answer to 2 decimal places.)

Answer 1

Solution :

x = 161

Using standard normal table,

P(Z > z) = 0.04

1 - P(Z < z) = 0.04

P(Z < z) = 1 - 0.04

P(Z < 1.751) = 0.96

z = 1.751

(a)

standard deviation = = 13

Using z-score formula,

= (x - z * ) = 161 - 1.751 * 13 = 138.24

Population mean = 138.24

(b)

standard deviation = = 24

Using z-score formula,

= (x - z * ) = 161 - 1.751 * 24 = 118.98

Population mean = 118.98

(c)

= 139

= (x - ) / z = (161 - 139) / 1.751 = 12.56

population standard deviation = = 12.56

(d)

= 122

= (x - ) / z = (161 - 122) / 1.751 = 22.27

population standard deviation = = 22.27