91影视

Given

$$\begin{gathered} p=67\% \\ =0.67 \end{gathered}$$

$x=62$

$n=100$

The sample proportion is the number of successes divided by the sample size:

$$\begin{gathered} \hat{p}=\frac{x}{n} \\ =\frac{62}{100} \\ =0.62 \end{gathered}$$

The mean of the sampling distribution of $\hat{p}$is equal to the population proportion $p$:

localid="1650095153168" $$\begin{gathered} {渭}_{\hat{p}}=p \\ =0.67 \end{gathered}$$

The standard deviation of the sampling distribution of $\hat{p}$is:

localid="1650095171714" $$\begin{gathered} {蟽}_{\hat{p}}=\sqrt{\frac{p(1-p)}{n}} \\ =\sqrt{\frac{0.67(1-0.67)}{100}} \\ 鈮�0.0470213 \end{gathered}$$

The z-score is the value decreased by the mean, divided by the standard deviation:

localid="1650095190764" $$\begin{gathered} z=\frac{x-渭}{蟽} \\ =\frac{0.62-0.67}{0.0470213} \\ 鈮�-1.06 \end{gathered}$$

Determine the corresponding probability using table A:

localid="1650095208985" $$\begin{gathered} P(\hat{p}鈮�0.62)=P(z<-1.06) \\ =0.1446 \end{gathered}$$

Given

$$\begin{gathered} p=67\% \\ =0.67 \end{gathered}$$

$x=62$

$n=100$

The sample proportion is the number of successes divided by the sample size:

$$\begin{gathered} \hat{p}=\frac{x}{n} \\ =\frac{62}{100} \\ =0.62 \end{gathered}$$

The mean of the sampling distribution of $\hat{p}$is equal to the population proportion $p$:

localid="1650095264695" $$\begin{gathered} {渭}_{\hat{p}}=p \\ =0.67 \end{gathered}$$

The standard deviation of the sampling distribution of $\hat{p}$is:

localid="1650095291522" $$\begin{gathered} {蟽}_{\hat{p}}=\sqrt{\frac{p(1-p)}{n}} \\ =\sqrt{\frac{0.67(1-0.67)}{100}} \\ 鈮�0.0470213 \end{gathered}$$

The z-score is the value decreased by the mean, divided by the standard deviation:

localid="1650095308205" $$\begin{gathered} z=\frac{x-渭}{蟽} \\ =\frac{0.62-0.67}{0.0470213} \\ 鈮�-1.06 \end{gathered}$$

Determine the corresponding probability using table A:

localid="1650095325932" $$\begin{gathered} P(\hat{p}鈮�0.62)=P(z<-1.06) \\ =0.1446 \end{gathered}$$