Need help, please.
I would like to know where does 1.96 come from?
on the solution.

Question

Need help, please. 
I would like to know where does 1.96 come from? 
on the solution.

loser66 · Answer

attachment

loser66 · Answer

About the standard error, Mistake is there and I knew it. $\sigma_M= \dfrac{\sigma}{\sqrt{n}}$

kropot72 · Answer

In a standardized normal distribution, 95% of the data points lie within the range plus and minus 1.96 standard deviations of the population mean.

loser66 · Answer

Got you. Thanks for that.
Another question: What if we apply the formula to find the solution?
I meant: $\bar x= 48.8$

loser66 · Answer

$P(47.8 \leq \bar x\leq 49.8)$ and use 

$P\left(\dfrac{47.8- \mu}{\sigma}\leq \dfrac{\bar x-\mu}{\sigma}\leq\dfrac{49.8-\mu}{\sigma}\right)=0.95$

to find the interval?

kropot72 · Answer

The worked example has used the "standard length of 49.0 in" in the calculation of the confidence interval. However it is usual to use the sample mean, x-bar, in the calculation. Using the sample mean, my result for the 95% confidence interval for the population mean is (48.45, 49.15).