Question

Q7. The height of persons is normally distributed with mean 61 inches and variance 25. It is known that 1.39% are taller persons. The height of the shortest person among the taller persons will be a. 5.5 feet b. 6.0 feet c. 6.5 feet d. 7.0 feet.

Answer 1

Solution:-

Given that,

mean = = 61 in.

variance = 2 = 25 in.

standard deviation = = 2 = 25 = 5 in.

Using standard normal table,

P(Z > z) = 1.39%

= 1 - P(Z < z) = 0.0139  

= P(Z < z) = 1 - 0.0139

= P(Z < z ) = 0.9861

= P(Z < 2.20 ) = 0.9861  

z = 2.20

Using z-score formula,

x = z * +

x = 2.20 * 5 + 61

x = 72 in.

x = 6.0 feet

correct option is = b