91影视

Fifty newborn elephants are weighed. The sample mean is $244$ pounds. The sample standard deviation is $11$ pounds.

If $\stackrel{炉}{x}$is the sample mean of a random sample of size $n$from a normal population with unknown variance ${蟽}^2$,

$\stackrel{炉}{x}-z_{\frac{伪}{2}}\frac{蟽}{\sqrt{n}}鈮�渭鈮�\stackrel{炉}{x}+z_{\frac{伪}{2}}\frac{蟽}{\sqrt{n}}$

where $z_{\frac{伪}{2}}$is the upper $100\frac{伪}{2}$percentage point of the standard normal distribution.

The standard deviation of the weights of elephants is known to be approximately $蟽=15$pounds. A random sample size $n=50$and a sample mean $\stackrel{炉}{x}=244$pounds.

We need find a $95\%$ confidence interval estimate for the population mean weight of newborn elephants. Therefore,

The previous implication was obtained on a probability table for the standard normal distribution.

From (1) and (2) we get

Therefore, $95\%\mathrm{Cl}$ for $渭$ is

We estimate with $95\%$confidence that the true population for weight of newborn elephants is between $239.84$and $248.16$

Ninety percent of all confidence intervals constructed in this way contain the true mean statistics exam score. For example, if we constructed $100$of these confidence intervals, we would expect $95$of them to contain the true population mean.

Confidence interval $CI=(239.84,248.16)$

The graph:

Error bpund$EBM:4.16$