2600 BUAL Final Exam Chen Yan

Consider a normal distribution with a mean of 300 and a variance of 15. What is the z value when x is 280?

-1.33

P (z > 1.25)

.1056

Suppose that historical sales records indicate that 40% of all customers who enter a discount department store make a purchase. What is the probability that two of the next three customers will make a purchase? Hint: Please use the table to answer the question.

.2880

P (0 < z < 1.25)

.4944

P (z < 1.25)

.8944

P (z = 1.25)

0

What is the median score of test 1?

12

What is the highest score of test 1?

21

What is the lowest score of test 1?

3

Data: 8,7,5,2,9,2,5,5 What is the mean?

38.6

Data: 8,7,5,2,9,2,5,5 What is the mode?

5

A random sample of size 36 is taken from a population with mean 50 and standard deviation 5. What is μ_x ̅ ?

= 5/ Square root of 36 = 5/6 =.833

A normal population has a 99.73 percent of the population measurements within ____________ standard deviation(s) of the mean.

A. 1 B. 2 C. 3 D. 4 C. 3

If n= 15 and p= .4, then the standard deviation of the binomial distribution is ___________.

A. 9 B. 6 C. 3.6 D. 1.897 D. 1.897

Let A,B and C be events and assume the following probabilities: P (A) = 0.2 , P(B) =0.3, P(C)= 0.5, P(ANB) = 0.06, P(ANC) = 0, P(BNC) = 0.5. Which two of the three events are mutually exclusive?

A. A,C B. A,B C. B,C A. A,C

Which of the following is a categorical variable?

A. Air temperature B. Bank account balance C. Daily sales in a store D. Whether a person has a traffic violation E. Value of company stock D. Whether a person has a traffic violation

________ says that if the sample size is sufficiently large, then the sample means are approximately normally distributed.

A. Cluster sampling B. Sampling error C. Sampling distribution of the mean D. The Central Limit Theorem D. The Central Limit Theorem

Which of the following is a type of question used in survey research?

A. Dichotomous B. Open-ended C. Multiple-choice D. All of the other answers are correct D. All of the other answers are correct

If two events are independent, we can _________ their probabilities to determine the intersection probability.

A. Divide B. Add C. Multiply D. Subtract C. Multiply

If a population distribution is skewed to the right, then, given a random sample from that population, one would expect that the _________.

A. Median would be equal to the mean B. Mode would be equal to the mean C. Median would be greater than the mean D. Median would be less than the mean D. Median would be less than the mean

The Central Limit Theorem states that as the sample size increases, the distribution of the sample ________ approaches the normal distribution.

A. Medians B. Means C. Standard deviations D. Variances B. Means

Which of the following is NOT a discrete random variable?

A. The number of times a light changes red in a 10-minute cycle B. The number of minutes required to run a mile C. The number of defects in a sample selected from a population of 100 products D. The number of criminals found in a five-mile radius of a neighborhood B. The number of minutes required to run a mile

The _________ of two events A and B is the event that consists of the sample space outcomes belonging to both event A and event B.

A. Union B. Intersection C. Complement D. Mutual Exclusivity B. Intersection

A standard normal distribution has a mean of ___________ and standard deviation of ___________.

A. Zero, zero B. Zero, one C. One, one D. One, zero B. Zero, one

The measurement in a sample or a population that occurs most frequently is the _________.

A. mode B. Mean C. Median D. Outlier E. Average A. Mode

Consider a normal population with a mean of 300 and a variance of 15. Find P (x < 280)

P (z < -1.33) .0918

If A and B are independent events, P(A) = .2 and P(B) = .7 determine P(AUB)

P(AUB)= P(A) + P(B) - P (ANB) .2 + .7 - (.2X.7) .9 - .14 =.76

An experiment has sample space S= {a, b, c, d, e}. The following table gives the probabilities for these outcomes, except P(c) is unknown. If we define the event E= {a, b, c}, What is P(E)?

P(E)= P(a) + P(b) + P(c) .2 + .1 + .15 = .45

The manager of the local grocery store has determined that, on average, 4 customers use the service desk every half-hour. Assume that the number of customers using the service desk has a Poisson distribution. What is the probability that during a randomly selected half-hour period, exactly 3 customers use the service desk? Hint: POISSON

P(x)= (E^-M X M^X) / (X!) =(2.71828^-4 X 4^3) / (3!) =0.1954

Describe the shape of the distribution

Skewed right

Assume that the finishing times in a New York City 10-kilometer road race are normally distributed with a mean of 61 minutes and a standard deviation of 9 minutes. Let X be a randomly selected finishing time. Find P (X > 72)

Z= (X-M) / Standard Deviation Z= (72-61) / 9 Z = 1.22 P (Z>1.22) =1-P(Z<1.22) =1-.8888 =.1112

How many outliers?

Zero