You'd like to estimate the proportion of students who attend Miami University on the Oxford campus who are graduate students. You poll a random sample of 150 students, of whom 17 are graduate students. Unknown to you, the proportion of all graduate students who attend Miami University on the Oxford campus is 0.123.
Describe the population distribution. Sketch a bar graph representing the population distribution.
Describe the data distribution. Sketch a bar graph representing the data distribution. Find the mean and standard deviation of the sampling distribution of the sample proportion for a sample of size 150. Explain what this sampling distribution represents. Sketch a graph representing this sampling distribution.

Question 3

A study reported that the length of pregnancy from conception to birth is approximately normally distributed with mean 272 days and standard deviation 9 days. Suppose we have a random sample of 100 women.

Source: Navidi, W., & Monk, B. (2022).Elementary Statistics (Fourth). McGraw Hill.

Define the Normal random variable.

State the Normal distribution parameters.

FindP(X>275). Be sure to also include a sketch. Explain what this probability means in context.

What is the shape of the sampling distribution of the sample mean?

Find the mean and standard deviation of the sampling distribution of the sample mean.

FindP(X>275). Be sure to also include a sketch. Explain what this probability means in context.

Explain the difference betweenP(X>275) andP(X>275).