Normal Distribution Examples

For each of the binomial distributions, compute the mean, variance, and standard deviation. n=600, p=0.52

Which of the following is not true regarding the normal probability distribution? (asymptotic, family of distributions, only two outcomes, 50 percent of the observations greater than the mean)

Binomial probability distributions depend on the number of trials n of a binomial experiment and the probability of success p on each trial. Under what conditions is it appropriate to use a normal approximation to the binomial?

Identify the distribution (normal, Student t, chi-square) that should be used in each of the fo llowing situations. If none of the three distributions can be used, what other method could be used? In constructing a confidence interval estimate of p, you have 1200 survey respondents and 5% of them answered "yes" to the first question.

The normal distribution is a good estimate for which of the binomial distributions. n=50, p=0.7

The answers to the questions have distributions with different amounts of variability. Would you expect these questions to produce distributions with a lot of variability or very little variability? a. How tall are high school students? b. What are the scores on a hard math test? c. How much actual medicine is in each pill?

How many normal distributions are there? (1, 10, 30, 1,000, or infinite-pick one)

Discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. If two normal distributions have the same mean and standard deviation, then they have the same shape.

What relationship exists between the standard normal distribution and the box-plot methodology for describing distributions of data by means of quartiles? The answer depends on the true underlying probability distribution of the data. Assume for the remainder of this exercise that the distribution is normal. Can you now better understand why the inner and outer fences of a box plot are used to detect outliers in a distribution? Explain.

The normal distribution is a good estimate for which of the binomial distributions. n=200, p=0.08

When comparing two data sets, which is better: frequency distributions or relative frequency distributions? Why?

Consider two binomial distributions for 1,000 repeated Bernoulli trials-the first for trials with p=.15, and the second for trials with p=.85. How are the histograms for the two distributions related? Explain.

What can you say about distributions A and B if they have the same mean but the standard deviation of A is greater than that of B?

The heights of people of the same gender and similar ages follow Normal distributions reasonably closely. How about body weights? The weights of women aged 20 to 29 have mean 141.7 pounds and median 133.2 pounds. The first and third quartiles are 118.3 pounds and 157.3 pounds. Is it reasonable to believe that the distribution of body weights for women aged 20 to 29 is approximately Normal? Explain your answer.

Assume normal distributions in the following exercises. Find the value of z. 8% of the scores are to the right of z.

What does the sampling distribution of the sample variance look like if we sample from a population with an approximately normal distribution? Find out using the applet Sampling Distribution of the Variance (Mound Shaped Population) (at academic.cengage.com/statistics/wackerly) to complete the following. In the previous exercises in this section, you obtained simulated sampling distributions for the sample mean. All these sampling distributions were well approximated (for large sample sizes) by a normal distribution. Although the distribution that you obtained is mound-shaped, does the sampling distribution of the sample variance seem to be symmetric (like the normal distribution)?

Explain why it is likely that the distributions of the following variables will be normal: the diameter of bolts immediately after manufacture.

Two populations have normal distributions. The first has population standard deviation 2 and the second has population standard deviation 3. A random sample of 16 measurements from the first population had a sample mean of 20. An independent random sample of 9 measurements from the second population had a sample mean of 19. Test the claim that the population mean of the first population exceeds that of the second. Use a 5% level of significance. State the hypotheses.

The normal distribution is a good estimate for which of the binomial distributions. n=40, p=0.1

Consider two normal distributions, one with mean -4 and standard deviation 3, and the other with mean 6 and standard deviation 3. Answer true or false to each statement and explain your answers. a. The two normal distributions have the same shape. b. The two normal distributions are centered at the same place.