A large town has 600 kindergarteners. The heighgts of the kinergarten children a

Question

A large town has 600 kindergarteners. The heighgts of the kinergarten children are approximately normally distributed with a mean height of 39 inches, and a standard deviation of 2 inches.

a) If a child is selected at random, what is the probability that her/his height is more than 39.5 inches?

b) Suppose a classroom of 36 children is used as a sample. Will we need the population correction factor if we consider an average height of the group?

c) What is the probability that the class' means height is taller than 39.5 inches?

Explanation / Answer

mean is 39 and s is 2

a) z is given as (x-mean)/s thus P(x>39.5) =P(z>(39.5-39)/2)=P(z>0.25) or 1-P(z<0.25), from normal distribution table we get 1-0.5987=0.4013

b) for 36 sample size, the standard error is s/sqrt(N)=2/sqrt(36)=0.3333

thus, we would need to find the new sample standard deviation

c) P(xbar>39.5)=P(z>(39.5-39)/0.3333)=P(z>1.5) or 1-P(z<1.5), from normal distribution table we get 1-0.9332=0.0668

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