Question

The heights (measured in inches) of men aged 20 to 29 follow approximately the normal distribution with mean 69.3 and standard deviation 2.8. Between what two values does that middle 92% of all heights fall? (Please give responses to 3 decimal places) what formula is used here?

Answer 1

Solution :

Given that,

mean = = 69.3

standard deviation = = 2.8

Using standard normal table,

P(-z < Z < z) = 92%
P(Z < z) - P(Z < z) = 0.92
2P(Z < z) - 1 = 0.92
2P(Z < z ) = 1 + 0.92
2P(Z < z) = 1.92
P(Z < z) = 1.92 / 2
P(Z < z) = 0.96
z =1.751 znd z = - 1.751

Using z-score formula,

x = z * +

x = 1.751 * 2.8 + 69.3

= 74.203

x = 74.203

x = z * +

x = - 1.751 *2.8 + 69.3

= 64.397

x = 64.397