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In: Statistics and Probability

Assume the population mean IQ is 100 with a standard deviation of 15. A sample of...

Assume the population mean IQ is 100 with a standard deviation of 15. A sample of 25 students recently took an IQ test in which their average score was 108. If another sample of 25 students was selected, what is the probability that that sample would have a mean greater than 108?

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Expert Solution

Solution :

Given that ,

mean = = 100

standard deviation = = 15

n = 25

= 100 and

= / n = 15 / 25 = 15 / 5 = 3

P(? > 108) = 1 - P( < 108) = P(( - ) / < (108 - 100) / 3) = 1 - P(z < 2.67)

Using standard normal table,

P( >108 ) = 1 - 0.9962 = 0.0038

Probability = 0.0038

orchestra answered 2 years ago
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