stats test

1. A discrete probability distribution for which the relative frequency method is used to assign the probabilities is known as the a. Discrete uniform probability distribution. b. Binomial probability distribution. c. Empirical probability distribution. d. Poisson probability distribution.

C. Empirical probability distribution.

1. A probability near 0 indicates that an event or outcome is likely to occur.

False

10. One major difference between the counting rule for combinations and the counting rule for permutations is that with combinations, order of selection is important.

False

17. The standard deviations of all normal random variables must equal one.

False

19. A random variable with Poisson distribution is an example of a continuous random variable.

False

20. Probabilities for any random variable, regardless of what values its mean and STD equal can be found by converting to z-scores and using the standard normal cumulative probability table.

False

21. Two required conditions for a discrete probability function, pdf, f(x) are 1) f(x) must be positive and 2) sum of f(x) across all possible outcomes of the random variable equals 1.

False

3. For a continuous random variable X, the value of probability density function at X = a, f(a), is the probability that X = a.

False

113. The PDF for all discrete random variables must be greater than or equal to zero and less than or equal to one.

True

14. Probabilities for all normally distributed random variables may be calculated by first transforming the random variable to its z-score and using the standard normal cumulative probability distribution table (aka "the Standard Normal table").

True

16. For any normal random variable X with mean = 0 and STD=, P(X < - σ) = P(X > σ).

True

18. A random variable that describes the number of patients a nurse sees per hour is a discrete random variable.

True

2. For a discrete random variable X, the sum of probabilities across all possible outcomes must equal one

True

4. For standard normal random variable Z, P(Z < -1) = P(Z > 1).

True

8. Probability is a numerical measure between 0 and 1 quantifying the likelihood that an event or particular outcome will occur.

True

9. A sample space is the set of all individuals or elements randomly selected from a population.

True

14. For the standard normal probability distribution, what is the z-value corresponding to a one-tail (upper) probability of 5%? a. 1.65 b. 1.96 c. 2.33 d. 1

a. 1.65

5. More than 50 million guests stay at bed and breakfasts (B&Bs) each year. The website for the Bed and Breakfast Inns of North America averages five visitors per minute and enables many B&Bs to attract guests. What probability distribution would you use to estimate the probability that the website has two or more visitors in the next one-minute period? a. Discrete uniform probability distribution. b. Binomial probability distribution. c. Empirical distribution d. Poisson probability distribution.

a. Discrete uniform probability distribution.

7. From a group of six people, two individuals are to be selected at random. How many possible pair selections are possible? a. 15 b. 8 c. 12 d. 36

a. 15

16. For a normal random variable, X, with mean = 4 and STD =2, what is the probability that X is in the area to left of the mean? a. -0.5. b. 0.5 c. any value between 0 to 1 d. 1

b. 0.5

6. NCAA estimates that the average yearly value of a full athletic scholarship at in-state public universities like CSULB is $19,000 (WSJ, March 12, 2012). Assume the yearly athletic scholarship value is normally distributed with a STD of $2,100. For a scholarship of $17,758, what must be true about its z-score? a. z-score > 0 b. z-score = 0 c. z-score < 0 d. 0 < z-score < 1

c. z-score < 0

9. For the standard normal probability distribution, the area to the right of the mean is given by a. 1.00 b. 3.09 c. 1.96 d. 0.50

d. 0.50

4. The highest point of a normal curve occurs at a. two standard deviations to the right of the mean b. the top of Mt. Everest. c. one standard deviation to the right of the mean. d. the mean.

d. the mean.

Suppose an environmental company is interested in building a pen to house and fertilize salmon along the Deschuttes river in Oregon. Suppose the shape of the histogram of returning salmon length contained in last year's data is bell-shaped. What probability distribution should she use to estimate the length (head to tail) of salmon who return in following years to spawn.? a. Uniform distribution b. Normal distribution c. Discrete uniform d. Binomial

B. normal distribution

12. For any discrete random variable X, the probability X assumes any value between a and b, (i.e., P(a < X < b)) is equal to the area under probability density function, f(x), between a and b.

True

22. Let X = ethnicity of a job applicant to Franklin Investment Co. Then X is a discrete random variable.

True

5. A discrete random variable X has outcomes consisting only of a finite set of distinct/individual values.

True

6. For a continuous random variable X, P(X ≤ a) = P(X < a) for a real number, a

True

7. For a discrete random variable, X, with the set of outcomes equal to the set of non-negative even integers = (0, 2, 4, 6, 8,10...), the probability that X assumes any value between and including 2 but strictly less than 10, P(2 ≤ X < 10) is given by ... P(2 ≤ X < 10) = P(X=2) + P(X=4)+ P(X=6)+ P(X=8)+ P(X=10).

True

7. For a continuous random variable X, the value of the probability density function at X = a is a. is equal to 0 since P(X=a) =0 for all numbers, a. b. is greater than 0. c. is greater than 0 but less than one or equal to 1. d. a cat.

a. is equal to 0 since P(X=a) =0 for all numbers, a.

8. Which one of these variables is a discrete random variable? a. X=number of unbroken eggs in a carton b. X=time it takes a randomly selected student to complete a multiple choice exam(in minutes) c. X=amount of pizza eaten by a random sample of students (measured in ounces). d. X=proportion of male births in the world

a. X=number of unbroken eggs in a carton

12. Let X be a random variable equal to the number of IS 310students that ace the second midterm. Suppose previous data suggests that probability of acing exam 2 is 0.1. If there are 40 people taking the exam. How many IS310 students do you predict will ace the test? a. 0 b. 4 c. 3.5 d. 36

b. 4

18. For the r.v. z with the standard normal probability distribution, what is the probability associated with -1.00 ≤ z ≤ 1.00? a. 0.3432 b. 0.6827 c. 0.8413 d. 0.1587

b. 0.6827

15. For the standard normal random variable, z, what probability range is associated with the area between z= -1.96 and 1.96? a. 0.90 b. 0.95 c. 0.99 d. 0.99

b. 0.95

17. For the standard normal probability distribution, what z-value, z0, corresponds to P(Z >z0) =.95. a. 1.96 b. 1.65 c. -1.65 d. -1.96

b. 1.65

4. A CSULB study reported that last year 15% of those who have signed up for "P91-Extreme Workout" ended up quitting before the course is over and vowing never to exercise again. What probability distribution would you use to calculate the probability that exactly 5 of the 30 gym members enrolled in P91will quit? a. Discrete uniform probability distribution. b. Binomial probability distribution. c. Empirical distribution. d. Poisson probability distribution.

b. Binomial probability distribution.

2. Which of the following is NOT a property of a discrete probability distribution function, f(x)? a. f(x) > 0 for all possible outcomes b. If x < 0 then f(x) =0 c. f(x) ≤ 1 d. ∑f(x)=1 for all possible outcomes

b. If x < 0 then f(x) =0

3. Probability is defined as .... a. a numerical measure between 0 and 1 that characterizes the chance that a random variable will assume a particular outcome greater than or equal to zero divided by the total number of outcomes possible. b. a numerical measure between 0 and 1 that quantifies the likelihood that an event or particular outcome occurs. c. a function of a random variable that results from the sum of relative frequencies of all possible outcomes in the sample space. d. the answer to the question, "Will you pass IS310 this term?"

b. a numerical measure between 0 and 1 that quantifies the likelihood that an event or particular outcome occurs.

5. In the standard normal distribution, the a. mean and the standard deviation are both 1. b. mean is 0 and the standard deviation is 1. c. mean is 0 and the standard deviation can have any value greater than 0. d. mean is "really mean" and the standard deviation is "a true deviant."

b. mean is 0 and the standard deviation is 1.

10. Consider a binomial experiment with n=10 and p=.3. Compute the probability that X= 0? a. 0 b. 0.7^10 c. 0.3^10 d. 0.7^0 = 1

b. 0.7^10

9. Which of the following is a discrete random variable? a. X=amount of mercury found in fish caught in the Gulf of Mexico (in mg3/kg2) b. X= 0 if "male", X=1 if "female", X=2 if "other" or "decline to state " c. X=amount of gasoline purchased by a customer (in gallons) d. X=height of water-oak trees (in meters)

b. X= 0 if "male", X=1 if "female", X=2 if "other" or "decline to state "

19. For the standard normal probability distribution, what is the z-score for an upper-tail probability of .025? a. 1.65 b. -1.96 c. 1.96 d. -2.33

c. 1.96

12. For normal distributions which of the following is NOT true regarding the probability density function (pdf), f(x)? a. As the standard deviation increases, the graph of the pdf, f(x), flattens and becomes wider. b. As the mean increases, so does central location of the pdf, f(x). c. The value of the pdf, f(x), is the same for each value of x. d. The value of the pdf, f(x), is different for various values of x.

c. The value of the pdf, f(x), is the same for each value of x.

20. Which of the following is not a random variable? a. X=number of chocolate chips in a Mrs. Field's cookie. b. X=length of time it takes for runners to finish a 10K race. c. X=Hair color d. X=Daily maximum temperature

c. X=Hair color

8. For any continuous random variable X with mean = μ and STD = σ the probability that X = μ is ... a. 0.5. b. more than one since it is continuous. c. a value larger than zero. d. 0.

c. a value larger than zero.

6. The standard deviation of a normal distribution a. must be between 0 and 1. b. is always 1. c. can be any value. d. cannot be negative.

c. can be any value.

11. For a random variable X distributed uniformly on the interval [- 2, -1.5], let f(x) be the pdf for X. Then which of the following is true? a. f(x) = -2 for -2 x -1.5. b. 0 f(x) 1. c. f(x) =2 for -2 x -1.5. d. f(x) is undefined since x < 0.

c. f(x) =2 for -2 x -1.5.

10. A negative value for a z-score indicates that a. a mistake has been made in computations, since z cannot be negative. b. the original observation is to the right or above the mean. c. the original observation is to the left or below the mean. d. the data have a negative mean.

c. the original observation is to the left or below the mean.

13. Larger values of the standard deviation result in a normal curve that is a. skewed to the right. b. skewed to the left c. wider and flatter d. narrower and more peaked

c. wider and flatter

11. Consider a normally distribution random variable, X, with mean=10 and STD = 5. Compute the probability that X=15. a. 0 b. 0.68 c. -0.84 d. 0.84

d. 0.84

3. Suppose a tutoring center wants to estimate the probability of randomly choosing a particular student from the class list. What probability distribution would you recommend? a. Normal distribution b. Discrete uniform c. Poisson d. Binomial

d. Binomial

11. The PDF for all continuous random variables must be greater than or equal to zero and less than or equal to one.

true

15. The probability for of any discrete random variable must be greater than or equal to zero and less than or equal to one.

true