\(np = 25(0.15)\)

\(np = 3.75\)

\(nq=25(1-0.15)\)

\(nq=21.25\)

Since both the values np and nq are not greater than 5, hence, we cannot approximate the \(\hat{p}\) distribution by a normal distribution.

asked 2020-10-21

(a) Suppose \(n = 100\) and \(p= 0.23\). Can we safely approximate the \(\hat{p}\) distribution by a normal distribution? Why?

Compute \(\mu_{\hat{p}}\) and \(\sigma_{\hat{p}}\).

asked 2021-02-16

(b) Suppose \(n= 20\) and \(p=0.23\). Can we safely approximate the \(\hat{p}\) distribution by a normal distribution? Why or why not?

asked 2021-02-13

(a) Suppose \(n = 33\) and \(p = 0.21\). Can we approximate the \(\hat{p}\)

distribution by a normal distribution? Why? What are the values of \(\mu_{\hat{p}}\) and \(\sigma_ {\hat{p}}\).?

asked 2020-11-05

Basic Computation:\(\hat{p}\) Distribution Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us.

(c) Suppose \(n = 48\) and \(p= 0.15\). Can we approximate the \(\hat{p}\) distribution by a normal distribution? Why? What are the values of \(\mu_{hat{p}}\) and \(\sigma_{p}\).?

(c) Suppose \(n = 48\) and \(p= 0.15\). Can we approximate the \(\hat{p}\) distribution by a normal distribution? Why? What are the values of \(\mu_{hat{p}}\) and \(\sigma_{p}\).?

asked 2021-01-27

p (at least 11) = ?

asked 2021-06-05

Use the following Normal Distribution table to calculate the area under the Normal Curve (Shaded area in the Figure) when \(Z=1.3\) and \(H=0.05\);

Assume that you do not have vales of the area beyond \(z=1.2\) in the table; i.e. you may need to use the extrapolation.

Check your calculated value and compare with the values in the table \([for\ z=1.3\ and\ H=0.05]\).

Calculate your percentage of error in the estimation.

How do I solve this problem using extrapolation?

\(\begin{array}{|c|c|}\hline Z+H & Prob. & Extrapolation \\ \hline 1.20000 & 0.38490 & Differences \\ \hline 1.21000 & 0.38690 & 0.00200 \\ \hline 1.22000 & 0.38880 & 0.00190 \\ \hline 1.23000 & 0.39070 & 0.00190 \\ \hline 1.24000 & 0.39250 & 0.00180 \\ \hline 1.25000 & 0.39440 & 0.00190 \\ \hline 1.26000 & 0.39620 & 0.00180 \\ \hline 1.27000 & 0.39800 & 0.00180 \\ \hline 1.28000 & 0.39970 & 0.00170 \\ \hline 1.29000 & 0.40150 & 0.00180 \\ \hline 1.30000 & 0.40320 & 0.00170 \\ \hline 1.31000 & 0.40490 & 0.00170 \\ \hline 1.32000 & 0.40660 & 0.00170 \\ \hline 1.33000 & 0.40830 & 0.00170 \\ \hline 1.34000 & 0.41010 & 0.00180 \\ \hline 1.35000 & 0.41190 & 0.00180 \\ \hline \end{array}\)

Assume that you do not have vales of the area beyond \(z=1.2\) in the table; i.e. you may need to use the extrapolation.

Check your calculated value and compare with the values in the table \([for\ z=1.3\ and\ H=0.05]\).

Calculate your percentage of error in the estimation.

How do I solve this problem using extrapolation?

\(\begin{array}{|c|c|}\hline Z+H & Prob. & Extrapolation \\ \hline 1.20000 & 0.38490 & Differences \\ \hline 1.21000 & 0.38690 & 0.00200 \\ \hline 1.22000 & 0.38880 & 0.00190 \\ \hline 1.23000 & 0.39070 & 0.00190 \\ \hline 1.24000 & 0.39250 & 0.00180 \\ \hline 1.25000 & 0.39440 & 0.00190 \\ \hline 1.26000 & 0.39620 & 0.00180 \\ \hline 1.27000 & 0.39800 & 0.00180 \\ \hline 1.28000 & 0.39970 & 0.00170 \\ \hline 1.29000 & 0.40150 & 0.00180 \\ \hline 1.30000 & 0.40320 & 0.00170 \\ \hline 1.31000 & 0.40490 & 0.00170 \\ \hline 1.32000 & 0.40660 & 0.00170 \\ \hline 1.33000 & 0.40830 & 0.00170 \\ \hline 1.34000 & 0.41010 & 0.00180 \\ \hline 1.35000 & 0.41190 & 0.00180 \\ \hline \end{array}\)

asked 2021-09-12

Suppose the ages of students in Statistics 101 follow a normal distribution with a mean of 23 years and a standard deviation of 3 years. If we randomly sampled 100 students, which of the following statements about the sampling distribution of the sample mean age is incorrect.

A) The expected value of the sample mean is equal to the populationâ€™s mean.

B) The standard deviation of the sampling distribution is equal to 3 years.

C) The shape of the sampling distribution is approximately normal.

D) The standard error of the sampling distribution is equal to 0.3 years.

A) The expected value of the sample mean is equal to the populationâ€™s mean.

B) The standard deviation of the sampling distribution is equal to 3 years.

C) The shape of the sampling distribution is approximately normal.

D) The standard error of the sampling distribution is equal to 0.3 years.