Question 765714: Kindergarten children have heights that are approximately normally distributed about a mean of 39.9 inches and a standard deviation of 2.3 inches. If a random sample of 25 is taken, what is the probability that the sample of kindergarten children has a mean height of less than 37.9 inches?
I need help with the set-up/formula to try to figure out how to solve this problem. Thanks in advance!
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! Kindergarten children have heights that are normally distributed about a mean of 39.9 inches and a standard deviation of 2.3 inches. If a random sample of 25 is taken, what is the probability that the sample of kindergarten children has a mean height of less than 37.9 inches?
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The mean for the population is the same as the mean for the sample, however, the standard deviation for the sample is = standard deviation / sqrt(n) where n is the sample size.
mean for the sample is 39.9 inches
standard deviation for the sample = 2.3 / sqrt(25) = .46
the associated z-value for height < 37.9 is (37.9 - 39.9) / .46 = -4.35
we consult the negative z tables for the probability associated with the z-value = -4.35
Pr(x<37.9) = 0.0000
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note that for values of z ≤ -3.90, the areas are 0.0000 to four decimal places
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