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Chapter 6: Q6 (page 289)

Using Normal Approximation. In Exercises 5–8, do the following: If the requirements of np⩾5andnq⩾5are both satisfied, estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution; ifnp<5or nq<5, then state that the normal approximation should not be used.

Births of BoysWithbirths and p= 0.512 for a boy, find P(Exactly 5 boys)

Short Answer

Expert verified

The normal approximation method cannot be used as np<5and nq<5.

Step by step solution

01

Given information

A sample of 8 births is considered. The proportion of boys (p) is equal to 0.512.

02

Check the requirement necessary for normal approximation

It is required that np⩾5andnq⩾5 .

The values are computed below:

np=80.512=4.10<5

nq=81-0.512=3.90<5

As the requirement is not fulfilled, the normal approximation cannot be applied to compute the probability value.

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Most popular questions from this chapter

Births There are about 11,000 births each day in the United States, and the proportion of boys born in the United States is 0.512. Assume that each day, 100 births are randomly selected and the proportion of boys is recorded.

a. What do you know about the mean of the sample proportions?

b. What do youknow about the shape of the distribution of the sample proportions?

Distributions In a continuous uniform distribution,

μ=minimum+maximum2   andσ=range12

a. Find the mean and standard deviation for the distribution of the waiting times represented in Figure 6-2, which accompanies Exercises 5–8.

b. For a continuous uniform distribution with μ=0   and   σ=1, the minimum is-3 and the maximum is 3. For this continuous uniform distribution, find the probability of randomly selecting a value between –1 and 1, and compare it to the value that would be obtained by incorrectly treating the distribution as a standard normal distribution. Does the distribution affect the results very much?

Birth Weights Based on Data Set 4 “Births” in Appendix B, birth weights are normally distributed with a mean of 3152.0 g and a standard deviation of 693.4 g.

a. For the bell-shaped graph, what is the area under the curve?

b. What is the value of the median?

c. What is the value of the mode?

d. What is the value of the variance?

Standard normal distribution. In Exercise 17-36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, Draw a graph, then find the probability of the given bone density test score. If using technology instead of Table A-2, round answers to four decimal places.

Less than 1.28

Unbiased Estimators Data Set 4 “Births” in Appendix B includes birth weights of 400 babies. If we compute the values of sample statistics from that sample, which of the following statistics are unbiased estimators of the corresponding population parameters: sample mean; sample median; sample range; sample variance; sample standard deviation; sample proportion?
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