Question

Can you please help me solve this questions. I want a clear explanation thank you.

Answer 1

Given:

`\begin{gathered} \text{Mean}=\mu=21.4 \\ \text{Standard deviation=}\sigma=5.0 \\ \text{Smple size=n=66} \end{gathered}`

The z-score for 90 percent is 1.64.

To find the 90 percent confidence interval,

`\begin{gathered} \mu+(\frac{\sigma}{\sqrt[]{n}}*1.64)=21.4+(\frac{5}{\sqrt[]{66}}*1.64) \\ =21.4+1.0094 \\ =22.4094\ldots\ldots(\text{ upper limit)} \\ \text{And} \\ \mu-(\frac{\sigma}{\sqrt[]{n}}*1.64)=21.4-(\frac{5}{\sqrt[]{66}}*1.64) \\ =21.4-1.0094 \\ =20.3906\ldots\ldots\ldots(\text{lower limit)} \end{gathered}`

Answer: The 90 % confidence interval is ( 20.3906 , 22.4094 )