91影视

Given

$$\begin{gathered} p=90\% \\ =0.90 \end{gathered}$$

$x=86$

$n=100$

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

$$\begin{gathered} \hat{p}=\frac{x}{n} \\ =\frac{86}{100} \\ =0.86 \end{gathered}$$

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

localid="1650094798455" $$\begin{gathered} {渭}_{\hat{p}}=p \\ =0.90 \end{gathered}$$

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

localid="1650094821910" $$\begin{gathered} {蟽}_{\hat{p}}=\sqrt{\frac{p(1-p)}{n}} \\ =\sqrt{\frac{0.90(1-0.90)}{100}} \\ =0.03 \end{gathered}$$

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

localid="1650094847207" $$\begin{gathered} z=\frac{x-渭}{蟽} \\ =\frac{0.86-0.90}{0.03} \\ 鈮�-1.33 \end{gathered}$$

Determine the corresponding probability using table A:

localid="1650094869728" $$\begin{gathered} P(\hat{p}鈮�0.86)=P(z<-1.33) \\ =0.0918 \end{gathered}$$

Given

$$\begin{gathered} p=90\% \\ =0.90 \end{gathered}$$

$x=86$

$n=100$

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

$$\begin{gathered} \hat{p}=\frac{x}{n} \\ =\frac{86}{100} \\ =0.86 \end{gathered}$$

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

localid="1650094921335" $$\begin{gathered} {渭}_{\hat{p}}=p \\ =0.90 \end{gathered}$$

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

localid="1650094942237" $$\begin{gathered} {蟽}_{\hat{p}}=\sqrt{\frac{p(1-p)}{n}} \\ =\sqrt{\frac{0.90(1-0.90)}{100}} \\ =0.03 \end{gathered}$$

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

localid="1650094966222" $$\begin{gathered} z=\frac{x-渭}{蟽} \\ =\frac{0.86-0.90}{0.03} \\ 鈮�-1.33 \end{gathered}$$

Determine the corresponding probability using table A:

localid="1650094986566" $$\begin{gathered} P(\hat{p}鈮�0.86)=P(z<-1.33) \\ =0.0918 \end{gathered}$$