Chapter 6QUIZ

TRUE OR FALSE

Question 6.445

1. True or false: The following is a continuous and not a discrete random variable: The amount of coffee in your next cup of coffee.

Question 6.446

2. True or false: The following is an example of a binomial experiment: Rolling a pair of dice three times and observing the sum of the two dice.

Question 6.447

3. True or false: Our distributions for continuous random variables are for samples and not for populations.

FILL IN THE BLANK

Question 6.448

4. The probability that a randomly chosen value of a normally distributed random variable will be greater than the mean is __________ .

Question 6.449

5. The probability that a randomly chosen value of a normally distributed random variable will be equal to the mean is __________ .

Question 6.450

6. The standard deviation of a normal random variable can never take a value that is less than __________ .

SHORT ANSWER

Question 6.451

7. Is the following a discrete or continuous random variable: the number of goals your college soccer team will score in its next game.

Question 6.452

8. Recording the gender of the next 20 babies born at City Hospital is an example of what kind of experiment?

Question 6.453

9. What are the values for the mean and standard deviation of the standard normal distribution?

CALCULATIONS AND INTERPRETATIONS

Question 6.454

10. CEOs Driving Luxury Cars. According to CareerBuilder.com, 19% of company CEOs drive luxury cars. Suppose a random sample is taken of 100 company CEOs.

  1. Find the probability that the sample contains 20 CEOs who drive luxury cars.
  2. What is the most likely number of CEOs who drive luxury cars?
  3. Find the mean, variance, and standard deviation. Interpret the mean.
  4. Suppose the sample contains 40 CEOs who drive luxury cars. Is this unusual? Explain how you determine this.

Question 6.455

11. Gambling Losses. Treatment providers for problem gamblers report that men who approached them for intervention had lost a mean of $2849 in the preceding four weeks, according to a 2002 report.22 Assume that the distribution of gambling losses is normally distributed with mean and standard deviation .

  1. Find the probability that a randomly selected male had lost more than $4000.
  2. What percentage of males lost between $3000 and $4000?
  3. Suppose that a gambling support group is trying to identify those who lose the most, as measured by the 95th percentile. How much money in gambling losses does this represent?
  4. Suppose you know of a male problem gambler who lost $1000 in four weeks and then approached a treatment provider. Is this amount unusual? On what do you base your answer?

Question 6.456

12. South Dakota Speeds. The National Motorists Association reports that, in South Dakota, the mean speed on interstate highways is 68.3 mph. Denote the mean to be , and assume that the distribution is normal and .

393

  1. Find the probability that a randomly chosen vehicle is traveling faster than the 65 mph speed limit.
  2. What percentage of vehicles travel slower than 60 mph?
  3. What proportion of vehicles travel at speeds between 65 and 68.3 mph?
  4. The National Motorists Association asserts that speeding tickets should be issued only for drivers whose speeds exceed the 85th percentile. If the police in South Dakota followed this rule, then at what speed would they start handing out speeding tickets?
  5. Suppose that someone from South Dakota never drives faster than 55 mph on the interstate. Is this unusual? On what do you base your answer?