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Chapter 4: Q. AP1.2 (page 292)

A child is 40inches tall, which places her at the 90thpercentile of all children of similar age. The heights for children of this age form an approximately Normal distribution with a mean of 38inches. Based on this information, what is the standard deviation of the heights of all children of this age?

a. 0.20inch

b. 0.31inch

c. 0.65inch

d. 1.21inches

e. 1.56inches

Short Answer

Expert verified

The standard deviation of the heights of all children of this age is (e) 1.56inches.

Step by step solution

01

Given Information

We have been given that the height of a child is 40inches which places her at the 90thpercentile of all children of similar age. And the mean of the Normal distribution is 38inches.

02

Simplification

Let, z=(40-38)/s(where, s = standard deviation)

P(z<(40-38)/s)=0.90(given)

So, we get

P(z<1.2816)=0.90

So,

(40-38)/s=1.2816

2/1.2816=s

s=1.56

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