Probability and Statistics: Key Concepts and Applications
Classified in Mathematics
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Probability Distributions
Discrete Random Variables
- 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.
- Which of the following is not a characteristic of a binomial probability distribution?
- (A) Each trial has a finite number of possible outcomes.
- 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
- The number of arrivals of delivery trucks per hour at a loading station is an example of which of the following processes?
- (C) Poisson
- 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
- What is the expected value of the binomial distribution where n = 16 and p = 0.85?
- (D) 13.6
- What is the standard deviation of a binomial distribution where n = 16 and p = 0.20?
- (A) 1.6
- 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
- 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
- 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
- What is the mean of the uniform distribution from 15 to 65?
- (A) 40
- 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
- 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
- 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)
- The percentage of all possible confidence intervals that will contain the true population parameter is known as the
- (A) Confidence level
- Which of the following is not a way to reduce the margin of error?
- (C) Decrease the sample size.
- 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)
- Which of the following is not one of the conditions necessary to use σ?
- (C) μ is known
- 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
- 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)
- 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