Question

Given a normal distribution with μ equals=102 and σ equals= 25​, and given you select a sample of n equals 25

d) There is a 69​% chance that Upper X is above what​ value?

(Type an integer or decimal rounded to two decimal places as​ needed.)

Answer 1

Given that,

mean = = 102

standard deviation = = 25

n = 25

= 102

= / n = 25/ 25=5

Using standard normal table,

P(Z > z) = 69%

= 1 - P(Z < z) = 0.69

= P(Z < z ) = 1 - 0.69

= P(Z < z ) = 0.31

= P(Z <-0.50) = 0.31

z = -0.50

Using z-score formula  

= z * +

= -0.50*5+102

= 99.50