Question

14) IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. A sample of 10 people is selected at random. Find the probability that the mean IQ of people in the sample is greater than $103.

Round your answer to 4 decimal places.

Answer 1

ANSWER:

Given that,

IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. A sample of 10 people is selected at random. Find the probability that the mean IQ of people in the sample is greater than $103.

Mean = = 100

Standard deviation = = 15

Sample size = n = 10

The probability that the mean IQ of people in the sample is greater than $103

P(x > 103) = P((x-) / (/sqrt(n)) > (103-100) / (15/sqrt(10)))

P(x > 103) = P(z > 3 / 4.74341649)

P(x > 103) = P(z > 0.63)

P(x > 103) =1 - P(z < 0.63)

P(x > 103) =1 - 0.73565

P(x > 103) = 0.26435

P(x > 103) = 0.2644 (Rounded to four decimal places)

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