The heights of the kindergarten children (pages 146-147) are approximately norma
ID: 3227397 • Letter: T
Question
The heights of the kindergarten children (pages 146-147) are approximately normally distributed with mu = 39 and sigma = 2. a. If an individual kindergarten child is selected at random, what is the probability that he or she has a height between 38 and 40 inches? b. A classroom of 30 of these children is used as a sample. What is the probability that the class mean X is between 38 and 40 inches? c. If an individual kindergarten child is selected at random, what is the probability that he or she is taller than 40 inches? d. A classroom of 30 of these kindergarten children is used as a sample. What is the probability that the class mean X is greater than 40 inches?Explanation / Answer
as z score =(X-mean)/std deviation
a)P(38<X<40)=P(-0.5<X<0.5)=0.6915-0.3085 =0.3829
b)here std deviation of mean =2/(30)1/2 =0.3651
P(38<X<40)=P(-2.7386<X<2.7386)=0.9969-0.0031=0.9938
c)P(X>40)=1-P(X<40)=1-P(Z<0.5)=1-0.6915=0.3085
d)for average
P(X>40)=1-P(X<40)=1-P(Z<2.7386)=1-0.9969=0.0031
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