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Luden [163]
3 years ago
9

A commonly used IQ test is scaled to have a mean of 100 and a standard deviation 15. A school counselor was curious about the av

erage IQ of the students in her school and took a random sample of fifty students’ IQ scores. The average of these was 107.9. Find a 95% confidence interval for the student IQ in the school.
Mathematics
1 answer:
Licemer1 [7]3 years ago
4 0

Answer: (103.74,112.06)

Step-by-step explanation:

The confidence interval for population mean is given by :_

\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}

Given : Sample size : n= 50

Sample mean : \overline{x}=107.9

Standard deviation : \sigma=15

Significance level : \alpha: 1-0.95=0.5

Critical value : z_{\alpha/2}=1.96

Then the 95% confidence interval for the student IQ in the school will be :-

107.9\pm (1.96)\dfrac{15}{\sqrt{50}}\\\\\approx107.9\pm0.075\\\\=(107.9-4.16,107.9+4.16)=(103.74,112.06)

Hence, the 95% confidence interval for the student IQ in the school= (103.74,112.06)

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