 # The scores of a certain population on the Wechsler Intelligence Scale for children (WISC) are thought to be normally distributed with a mean and standard deviation of 10. The 95\% confidence interval for \mu is? UkusakazaL 2021-08-09 Answered
The scores of a certain population on the Wechsler Intelligence Scale for children (WISC) are thought to be normally distributed with a mean and standard deviation of 10. A simple random sample of twenty -five children from this population is taken and each is given the WISC. The mean of the twenty-five score is $\stackrel{―}{x}=104.32$. Based on these data a $95\mathrm{%}$ confidence interval for $\mu$ is computed.
The $95\mathrm{%}$ confidence interval for $\mu$ is?
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Step 1
Given:
$\sigma =10$
$\stackrel{―}{x}=104.32$
$n=25$
Step 2
The $95\mathrm{%}$ cocfidence interval for the mean is:
$C.I.=\stackrel{―}{x}±{Z}_{\frac{\alpha }{2}}×\frac{\sigma }{\sqrt{n}}$
From the Z table ${Z}_{\frac{\alpha }{2}}=1.96$
$=104.32±1.96×\frac{10}{\sqrt{25}}$

$=104.32±3.92$