Random Variables and Probability Models

Find the z-score for which the area under the standard normal curve to its left is 0.40 -0.25 0.57 0.25 -0.57

-.25

The average number of pushups a United States Marine does daily is 300, with a standard deviation of 50. A random sample of 36 Marines is selected. What is the probability that the sample mean is at most 320 push-ups? 0.0082 0.3446 0.6554 0.8767 0.9918

.99

IQ test scores are normally distributed with a mean of 96 and a standard deviation of 19. An individual's IQ score is found to be 125. Find the z-score corresponding to this value. -0.66 1.53 0.66 -1.53

1.53

Find the z-score for which the area under the standard normal curve to its left is 0.96 1.75 -1.38 1.82 1.03

1.75

Keeping in mind that a normal distribution is a model for a continuous variable, which one of the following variables cannot possibly have a normal distribution? A. People's opinions about a new tax law (favor or oppose) B. Weights of 5-year-old male children C. Handspans of adult females D. Ounces of soda in cans labeled as having 12 ounces

A

The peak shopping time at a home improvement store is between 8:00am-11:00am on Saturday mornings. Management at the home improvement store randomly selected 115 customers last Saturday morning and decided to observe their shopping habits. They recorded the number of items that each of the customers purchased as well as the total time the customers spent in the store. Identify the types of variables recorded by the home improvement store. A. number of items - discrete; total time - continuous B. number of items - continuous; total time - continuous C. number of items - continuous; total time - discrete D. number of items - discrete; total time - discrete

A

Which of the following is a true statement? A. The area under a normal curve is always equal to 1, no matter what the mean and standard deviation are. B. All bell-shaped curves are normal distributions for some choice of μ and σ. C. The smaller the standard deviation of a normal curve, the lower and more spread out the graph. D. Depending upon the value of the standard deviation, normal curves with different means may be centered around the same number. E. Depending upon the value of the standard deviation, the mean and median of a particular normal distribution may be different.

A

A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 440 seconds and a standard deviation of 60 seconds. Find the probability that a randomly selected boy in secondary school can run the mile in less than 302 seconds. .9893 .0107 .5107 .4893

B

The number of column inches of classified advertisements appearing on Mondays in a certain daily newspaper has mean 320 inches and standard deviation 30 inches. Suppose that the results for 100 consecutive Mondays can be regarded as a simple random sample and let X denote the mean number of column inches of classified advertisements in the sample. Assuming a sample of 100 is sufficiently large, the random variable X¯ has a distribution that is exactly normal by the central limit theorem. distribution that is approximately normal by the central limit theorem. mean of 3.2 inches by the law of large numbers. standard deviation of 3.2 inches by the law of large numbers. More than one is true.

B

Use the standard normal distribution to find P(-2.50 < z < 1.50). A..6167 B.9270 C. .8822 D. .5496

B

Which of the following is not a characteristic of the normal distribution? A. it is a symmetrical distribution B. the mean is always zero C. the mean, median and mode are equal D. it is a bell-shaped distribution e. the area under the curve equals one

B

Use the standard normal distribution to find P(0 < z < 2.25). A. .8817 B. .5122 C. .4878 D.7888

C

What is the distribution of values taken by a statistic in all possible samples of the same size from the same population called? the probability that the statistic is obtained. A. the population parameter. B. the variance of the values. C. the sampling distribution of the statistic. D. the distribution of sample data

C

Which one of the following probabilities is a cumulative probability? A. The probability that there are exactly 4 people with Type 0+ blood in a sample of 10 people. B. The probability of exactly 3 heads in 6 flips of a coin. C. The probability that the accumulated annual rainfall in a certain city next year, rounded to the nearest inch, will be 18 inches. D. The probability that a randomly selected woman's height is 67 inches or less.

C

Classify the following random variable according to whether it is discrete or continuous. The height of a player on a basketball team

Continuous

The Central Limit theorem for a sample mean is a critical result because A.it states that for large sample sizes, the population distribution is approximately normal. B.it states that for large sample sizes, the sample is approximately normal. C.it states that for any population, the sampling distribution is normal regardless of sample size. D.it states that for large sample sizes, the sampling distribution is approximately normal regardless of the population distribution. E.it states that for any sample size, the sampling distribution is normal.

D

Which of the following statements best describes the relationship between a parameter and a statistic? A. A parameter has a sampling distribution with the statistic as its mean. B. A parameter has a sampling distribution that can be used to determine what values the statistic is likely to have in repeated samples. C. A parameter is used to estimate a statistic. D. A statistic is used to estimate a parameter.

D

Which of the following statements is not correct concerning the probability distribution of a continuous random variable? A. the vertical coordinate is the probability density function B. the range of the random variable is found on the x-axis C. the total area represented under the curve will equal 1 D. the area under the curve between points a and b represents the probability that X = a E. the area under the curve represents the sum of probabilities for all possible outcomes

D

A random variable cannot be both continuous and discrete uniform normal skewed

Discrete

Classify the following random variable according to whether it is discrete or continuous. The number of cups of coffee sold in a cafeteria during lunch

Discrete

The daily revenue at a university snack bar has been recorded for the past five years. Records indicate that the mean daily revenue is $1500 and the standard deviation is $500. The distribution is skewed to the right due to several high volume days (football game days). Suppose that 100 days are randomly selected and the average daily revenue computed. Which of the following describes the sampling distribution of the sample mean? normally distributed with a mean of $1500 and a standard deviation of $500 normally distributed with a mean of $1500 and a standard deviation of $50 normally distributed with a mean of $150 and a standard deviation of $50 skewed to the right with a mean of $1500 and a standard deviation of $500

b