The heights of kindergarten children are approximately normally distributed with

Question

The heights of kindergarten children are approximately normally distributed with the following. (Give your answers correct to four decimal places.)

? = 37 and ? = 3.7 inches

(a) If an individual kindergarten child is selected at random, what is the probability that he or she has a height between 34.6 and 39.4 inches? (b) A classroom of 15 of these children is used as a sample. What is the probability that the class mean x is between 34.6 and 39.4 inches? (c) If an individual kindergarten child is selected at random, what is the probability that he or she is taller than 39.3 inches? (d) A classroom of 15 of these kindergarten children is used as a sample. What is the probability that the class mean x is greater than 39.3 inches?

Explanation / Answer

Ans:

Given that

? = 37 and ? = 3.7 inches

a)

z(34.6)=(34.6-37)/3.7=-0.649

z(39.4)=(39.4-37)/3.7=0.649

P(-0.649<z<0.649)=P(z<0.649)-P(z<-0.649)=0.7417-0.2583=0.4834

b)

z(34.6)=(34.6-37)*sqrt(15)/3.7=-2.51

z(39.4)=(39.4-37)*sqrt(15)/3.7=2.51

P(-2.51<z<2.51)=P(z<2.51)-P(z<-2.51)=0.9940-0.0060=0.9880

c)

z=(39.3-37)/3.7=0.622

P(z>0.622)=0.2671

d)

z=(39.3-37)*sqrt(15)/3.7

z=2.41

P(z>2.41)=0.0080

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