Question

Assume the length X of a certain unit follows the normal distribution with a mean of 50mm and a standard deviation of 5 mm. If a random sample of 21 units is taken, find the value C such that Probability(sample variance > C) = 0.90

Answer 1

Given that,

mean = = 50 mm

standard deviation = = 5 mm

n = 21

= = 50 mm

= / n = 5 / 21 = 1.09

Using standard normal table,

P(Z > z) = 0.90

= 1 - P(Z < z) = 0.90  

= P(Z < z ) = 1 - 0.90

= P(Z < z ) = 0.10

= P(Z < -1.28 ) = 0.10  

z = -1.28

Using z-score formula  

= z * +   

= -1.28 * 1.09 + 50

= 48.60 mm

C = 48.60 mm