Probability and Statistics: Key Concepts and Applications

Probability Distributions

Discrete Random Variables

1. If the outcomes of a discrete random variable follow a Poisson distribution, then which of the following is true?
   • (A) The mean equals the variance.
2. Which of the following is not a characteristic of a binomial probability distribution?
   • (A) Each trial has a finite number of possible outcomes.
3. If the probability of a machine producing a defective part is 0.05, what is the probability of finding exactly 5 defective parts from a sample of 100? (Assume that the process follows a binomial distribution and round the answer to four places.)
   • (C) 0.1800
4. The number of arrivals of delivery trucks per hour at a loading station is an example of which of the following processes?
   • (C) Poisson
5. When sampling without replacement from a finite population such that the probability of success, p, is no longer constant from trial to trial, the data follow a
   • (B) Hypergeometric distribution
6. What is the expected value of the binomial distribution where n = 16 and p = 0.85?
   • (D) 13.6
7. What is the standard deviation of a binomial distribution where n = 16 and p = 0.20?
   • (A) 1.6
8. A golfer routinely practices 15-foot putts, which he makes 25% of the time. What is the probability that he will make exactly 5 of his next 10 attempts?
   • (A) 0.0584

Continuous Random Variables

10. The mean weight of a sample of bags of potato chips is 5.5 ounces and the standard deviation is 0.2 ounces. What is the z-value of a bag that weighs 5.4 ounces?
    • (B) -0.5
11. Suppose random variable X has a normal distribution with a mean of 98.2 and the standard deviation of 3.2, find P(x ≥ 99).
    • (C) 0.4013
12. What is the mean of the uniform distribution from 15 to 65?
    • (A) 40
13. The speed of cars passing through a checkpoint follows a normal distribution with a mean of 62 miles per hour with a standard deviation of 4 miles per hour. What is the probability that the next car will be exceeding 57 miles per hour?
    • (C) 0.8944

Sampling and Confidence Intervals

1. The difference between a value (a statistic) computed from a sample and the corresponding value (a parameter) computed from the population is known as
   • (B) Sampling error
2. The average amount of cola in a sample of 80 bottles was 101.2 mL. An earlier study suggested that the standard deviation of the bottles is 1.4 mL. Determine the 95% confidence interval for the estimate of the population mean.
   • (C) (100.893, 101.507)
3. The percentage of all possible confidence intervals that will contain the true population parameter is known as the
   • (A) Confidence level
4. Which of the following is not a way to reduce the margin of error?
   • (C) Decrease the sample size.
5. Develop a 95% confidence interval for the mean when the sample mean is 90.3, the sample standard deviation is 11.6, and the sample size is 25. Assume the population is normally distributed.
   • (A) (85.512, 95.088)
6. Which of the following is not one of the conditions necessary to use σ?
   • (C) μ is known
7. A consumer group wishes to estimate the average electric bills for the month of July for single-family homes in a large city. Based on studies conducted in other cities, the population standard deviation is $25. The group wants to estimate the average bill for July to within $5 of the true average with 90% confidence. What sample size is needed?
   • (A) 68
8. A researcher found that 62 of the 85 people randomly selected were in favor of reducing the sales tax. Compute the 90% confidence interval estimate for π.
   • (D) (0.650, 0.808)
9. A researcher did a pilot sample of 25 individuals and found p to be 0.20. How many more must he survey to develop a 95% confidence interval that has a 0.03 margin of error?
   • (A) 658