Suppose babies born in a large hospital have a mean weight of 3200 grams, and a standard deviation of 526 grams. If 100 babies are sampled at random from the hospital, what is the probability that the mean weight of the sample babies would differ from the population mean by less than 50 grams?
Solution :
Given that,
mean = = 3200
standard deviation = = 526
n = 100
_{} = / n = 600 / 100 = 60
P(3150 < < 3250) = P((-50 / 60) / <( - _{}) / _{} < (50 / 60) / ))
= P(-0.83 < Z < 0.83)
= P(Z < 0.83) - P(Z < -0.83) Using z table,
= 0.5935
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