91影视

Good Sample? A geneticist is investigating the proportion of boys born in the world population. Because she is based in China, she obtains sample data from that country. Is the resulting sample proportion a good estimator of the population proportion of boys born worldwide? Why or why not?

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

Births of Boys With n = 20 births and p = 0.512 for a boy, find P(fewer than 8 boys).

Interpreting Normal Quantile Plots. In Exercises 5鈥�8, examine the normal quantile plot and determine whether the sample data appear to be from a population with a normal distribution.Ages of Presidents The normal quantile plot represents the ages of presidents of the United States at the times of their inaugurations. The data are from Data Set 15 鈥淧residents鈥� in Appendix B.

Foot Lengths of Women Assume that foot lengths of women are normally distributed with a mean of 9.6 in. and a standard deviation of 0.5 in., based on data from the U.S. Army Anthropometry Survey (ANSUR).

a. Find the probability that a randomly selected woman has a foot length less than 10.0 in.

b. Find the probability that a randomly selected woman has a foot length between 8.0 in. and 11.0 in.

c. Find$P_{95}=10.42\text{in}$

d. Find the probability that 25 women have foot lengths with a mean greater than 9.8 in.

Notation

a. Identify the values of $渭$ and $蟽$ for the standard normal distribution.

b. What do the symbols ${渭}_{\stackrel{炉}{x}}$ and ${蟽}_{\stackrel{炉}{x}}$represent?

In Exercises 5鈥�8, find the area of the shaded region. The graphs depict IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler IQ test).

Using the Central Limit Theorem. In Exercises 5鈥�8, assume that females have pulse rates that are normally distributed with a mean of 74.0 beats per minute and a standard deviation of 12.5 beats per minute (based on Data Set 1 鈥淏ody Data鈥� in Appendix B).

a.If 1 adult female is randomly selected, find the probability that her pulse rate is less than 80 beats per minute.

b. If 16 adult females are randomly selected, find the probability that they have pulse rates with a mean less than 80 beats per minute.

c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?

Distributions In a continuous uniform distribution,

$渭=\frac{minimum+maximum}{2}鈥�鈥�鈥�and蟽=\frac{range}{\sqrt{12}}$

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

b. For a continuous uniform distribution with $渭=0鈥�鈥�鈥�and鈥�鈥�鈥�蟽=1$, the minimum is$-\sqrt{3}$ and the maximum is $\sqrt{3}$. For this continuous uniform distribution, find the probability of randomly selecting a value between 鈥�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?

Hurricanes. In Exercises 5鈥�8, assume that the Poisson distribution applies; assume that the mean number of Atlantic hurricanes in the United States is 6.1 per year, as in Example 1; and proceed to find the indicated probability.

Hurricanes

a. Find the probability that in a year, there will be 5 hurricanes.

b. In a 55-year period, how many years are expected to have 5 hurricanes?

c. How does the result from part (b) compare to the recent period of 55 years in which 8 years had 5 hurricanes? Does the Poisson distribution work well here?

Notation

a. Identify the values of \(\mu \) and \(\sigma \) for the standard normal distribution.

b. What do the symbols \({\mu _{\bar x}}\) and \({\sigma _{\bar x}}\)represent?