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Chapter 7: Q 43. (page 464)
Students on diets Suppose that of college women have been on a diet
within the past months. A sample survey interviews an SRS of college women. What is the probability that or more of the women in the sample have been on a diet?
The probability is
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A study of rush-hour traffic in San Francisco counts the number of people in each car entering a freeway at a suburban interchange. Suppose that this count has mean 1.6 and standard deviation 0.75 in the population of all cars that enter at this interchange during rush hour.
a. Without doing any calculations, explain which event is more likely:
b. Explain why you cannot use a Normal distribution to calculate the probability of the first event in part (a).
c. Calculate the probability of the second event in part (a).
David鈥檚 iPod has about songs. The distribution of the play times for these songs is heavily skewed to the right with a mean of seconds and a standard deviation of seconds.
a. Describe the shape of the sampling distribution of for SRSs of size from the population of songs on David鈥檚 iPod. Justify your answer.
b. Describe the shape of the sampling distribution of for SRSs of size from the population of songs on David鈥檚 iPod. Justify your answer.
The number of flaws per square yard in a type of carpet material varies with mean flaws per square yard and standard deviation flaws per square yard.
a. Without doing any calculations, explain which event is more likely:
b. Explain why you cannot use a Normal distribution to calculate the probability of the first event in part (a).
c. Calculate the probability of the second event in part (a).
The central limit theorem is important in statistics because it allows us to use a Normal distribution to find probabilities involving the sample mean if the
a. sample size is reasonably large (for any population).
b. population is Normally distributed (for any sample size).
c. population is Normally distributed and the sample size is reasonably large.
d. population is Normally distributed and the population standard deviation is known (for any sample size).
e. population size is reasonably large (whether the population distribution is known or not).
78 refer to the following setting. In the language of government statistics, you are "in the labor force" if you are available for work and either working or actively seeking work. The unemployment rate is the proportion of the labor force (not of the entire population) that is unemployed. Here are estimates from the Current Population Survey for the civilian population aged 25 years and over in a recent year. The table entries are counts in thousands of people.
Unemployment Suppose that you randomly select one person 25 years of age or older.
a. What is the probability that a randomly chosen person 25 years of age or older is in the labor force?
b. If you know that a randomly chosen person 25 years of age or older is a college graduate, what is the probability that he or she is in the labor force?
c. Are the events "in the labor force" and "college graduate" independent? Justify your answer.
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