Question

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 average 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.

Answer 1

Answer: (103.74,112.06)

Explanation:

The confidence interval for population mean is given by :_

`\overline{x}\pm z_(\alpha/2)(\sigma)/(√(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)(15)/(√(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)