SOLUTION: The IQ test scores of adults are normally distributed with a mean of 100 and a standard deviation of 15. What is the probability that the mean IQ score in a random sample of 50 adu
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Question 1148148: The IQ test scores of adults are normally distributed with a mean of 100 and a standard deviation of 15. What is the probability that the mean IQ score in a random sample of 50 adults will be more than 95? Answer by rothauserc(4718) (Show Source):
You can put this solution on YOUR website! standard error of the sample = 15/square root(50) = 2.1213
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z-score(95) = (95 - 100)/2.1213 = −2.357 is approximately -2.36
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Probability (P) (X > 95) = 1 - P(X<95)
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P (X < 95) is found by looking in the z-tables for the probability associated with a z-score of -2.36, therefore
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P (X < 95) = 0.0091
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P (X > 95) = 1 - 0.0091 = 0.9909 is approximately 0.99
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