A random 2

A random sample of 40 families has an average water consumption of 29 cubic meters per month, with a sample standard deviation of 8 cubic meters. Give the 90% confidence interval for the mean usage of water per month.

Correct answer:

a =  26.9192 m³
b =  31.0808 m³

Step-by-step explanation:

$$\begin{gathered} n=40 \\ m=29{\text{m}}^3 \\ \sigma =8{\text{m}}^3 \\ p=90\%=\frac{90}{100}=\frac{9}{10}=0.9 \\ s=\frac{\sigma }{\sqrt{n}}=\frac{8}{\sqrt{40}}\doteq 1.2649 \\ (100-90)\%/2=5\% \\ {z}_0=1.645 \\ e=z_0\cdot s=1.645\cdot 1.2649\doteq 2.0808{\text{m}}^3 \\ a=m-e=29-2.0808=26.9192{\text{m}}^3 \end{gathered}$$

$b=m+e=29+2.0808=31.0808{\text{m}}^3$

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