Answered: Fill in the blanks. a. The mean of all…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.3: Special Probability Density Functions

Problem 53E

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Question

Fill in the blanks.

a. The mean of all possible sample proportions is equal to the_______.

b. For large samples, the possible sample proportions have approximately________a distribution.

c. A rule of thumb for using a normal distribution to approximate the

d. Distribution of all possible sample proportions is that both________and________are_________ or greater.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Expert Solution

Step 1

Introduction

A normal distribution is continuous distribution with a bell shaped curve.

Step 2

Sampling dist. of the sample prop.

The mean of $\hat{p}$ is equal to the pop. prop., $μ_{\hat{p}} = p$ i.e., the sample prop. is an unbiased estimator of the pop. prop.
The standard deviation of $\hat{p}$ is $σ_{\hat{p}} = \sqrt{\frac{p \times (1 - p)}{n}}$
For large n, $\hat{p}$ is approximately normally distributed.

Hence, the mean of all possible sample proportions is equal to the population proportion.

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