Question

Companies who design furniture for elementary school classrooms produce a variety of sizes for kids of different ages. Suppose the height of kindergarten children can be described by a Noal model with a mean of 39.2 inches and a standard deviation of 1.9 inches. In what height intervals should the company expect to find the middle 90%.

Answer 1

Solution :

mean = = 39.2

standard deviation = = 1.9

Using standard normal table,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

1 -   / 2 = 1 - 0.05 = 0.95

Z_/2 = Z _0.05 = 1.645

Z_{1 - /2} = Z _0.95 = -1.645

Using z-score formula,

x = z * +

x = -1.645 * 1.9 + 39.2 = 36.1 and

x = 1.645 * 1.9 + 39.2 = 42.3

Height intervals : (36.1 , 42.3)