SOLUTION: Given the normal distribution of children's ages in a preschool educational program where the mean is 4 years and the standard deviation is 1 year, what is the probability of rando

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Question 778331: Given the normal distribution of children's ages in a preschool educational program where the mean is 4 years and the standard deviation is 1 year, what is the probability of randomly selecting an age between 4 and 5? what is the z standard score of an age 5? what is the percentage of ages 5 and over? what is the probability of randomly selecting an age 2 and under?
Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
First calculate the Z-score.

For 5 yrs age the Z-score is Z+=+%28x+-+mu%29%2Fsigma+=+%285+-+4%29%2F1+=+1
For 4 yrs age the Z-score is Z+=+%28x+-+mu%29%2Fsigma+=+%284+-+4%29%2F1+=+0

The probability that the age of children is less than 5 years is
P%28x%3C5%29+=+P%28Z%3C1%29+=+0.84134

The probability that the age of children is less than 5 years is
P%28x%3C4%29+=+P%28Z%3C0%29+=+0.5

Using Standard Normal Distribution table, probability that the age of children lie between 4 and 5 years is given by
P%284%3Cx%3C5%29+=+0.84134-0.5=0.34134

Try the rest yourself. If you still need help then let me know.