AP Stats Final Review

Which score has the highest relative position: a score of 40 on a test with a mean of 31 and a standard deviation of 9, a score of 3.8 on a test with a mean of 2.5 and a standard deviation of 1.2 or a score of 491 on a test with a mean of 445 and a standard deviation of 46? (Assume that the distributions being compared have approximately the same shape.)

A score of 3.8

Find the sample standard deviation for the given data. Round your final answer to one more decimal place than that used or the observations. To get the best deal on a CD player, Tom called eight appliance stores and asked the cost of a specific model. The prices he was quoted are listed below: $142 $205 $303 $429 $140 $384 $330 $209

$109.6

The weekly salaries (in dollars) of sixteen government workers are listed below. Find the first quartile, Q1. 690 591 813 652 728 562 489 635 529 670 685 464 554 787 496 826

$541.50

Consider the following sample of exam scores, arranged in increasing order: 22 35 44 55 67 70 78 81 81 82 84 88 88 89 90 90 91 92 92 93 93 94 94 95 95 96 96 97 99 100 Note: The sample mean and sample standard deviation of these weights are, respectively, 82.4 and 19.5. (i) Use the Empirical rule to estimate the percentages of the observations that lie within 3 standard deviation(s) to either side of the mean. (ii) Use the data to obtain the exact percentages of the observations that lie within 3 standard deviation(s) to either side of the mean.

(i) Assuming that the scores have a roughly bell-shaped distribution, approximately 99.7% of the observations should lie within 19.5 points of the mean 82.4 or within the interval from 23.9 to 140.9; (ii) 29 of the 30 observations (96.7%) lie between 23.9 and 140.9.

A variable x has the possible observations shown below. Possible observations of x: -3 -1 0 1 1 2 4 4 5 Find the z-score corresponding to an observed value of x of -1. Round the values of μ and Η to one decimal place. Round your final answer to two decimal places.

-0.96

Use a table of areas for the standard normal curve to find the required z-score. Find the z-score having area 0.86 to its right under the standard normal curve; that is, find z 0.86 .

-1.08

Use a table of areas for the standard normal curve to find the required z-score. Determine the two z-scores that divide the area under the standard normal curve into a middle 0.874 area and two outside 0.063 areas.

-1.53, 1.53

Use a table of areas for the standard normal curve to find the required z-score. Find the z-score for which the area under the standard normal curve to its left is 0.04

-1.75

Use a table of areas for the standard normal curve to find the required z-score. Determine the two z-scores that divide the area under the standard normal curve into a middle 0.96 area and two outside 0.02 areas.

-2.05 and 2.05

The value obtained for the test statistic, z, in a one-mean z-test is given. Also given is whether the test is two tailed, left tailed, or right tailed. Determine the P-value. A left-tailed test: z = -2.65

0.0040

The value obtained for the test statistic, z, in a one-mean z-test is given. Also given is whether the test is two tailed, left tailed, or right tailed. Determine the P-value. A right-tailed test: z = 2.38

0.0087

The number of successes and the sample size are given for a simple random sample from a population. Use the one-proportion z-interval procedure to find the required confidence interval. n = 66, x = 12; 95% level

0.089 to 0.275

For the given hypothesis test, determine the probability of a Type II error or the power, as specified. A hypothesis test is to be performed to determine whether the mean waiting time during peak hours for customers in a grocery store has increased from the previous mean waiting time of 8.3 minutes. Preliminary data analyses indicate that it is reasonable to apply a z-test. The hypotheses are H 0: μ = 8.3 minutes H a: μ > 8.3 minutes. The population standard deviation is 3.6 minutes. The sample size is 45. The significance level is 0.05. Find the probability of a Type II error if in fact the mean waiting time, μ, is 9.8 minutes.

0.125

The value obtained for the test statistic, z, in a one-mean z-test is given. Also given is whether the test is two tailed, left tailed, or right tailed. Determine the P-value. A two-tailed test: z = 1.31

0.1902

In a certain class of students, there are 8 boys from Wilmette, 5 girls from Kenilworth, 10 girls from Wilmette, 4 boys from Glencoe, 3 boys from Kenilworth and 8 girls from Glencoe. If the teacher calls upon a student to answer a question, what is the probability that the student will be from Kenilworth?

0.211

The age distribution of students at a community college is given below. Age (years) Number of students (f) Under 21: 401 21-25: 407 26-30: 206 31-35: 57 Over 35: 20 1091 A student from the community college is selected at random. Find the probability that the student is between 26 and 35 inclusive. Round approximations to three decimal places.

0.241

Suppose one card is selected at random from an ordinary deck of 52 playing cards. Let A = event a queen is selected B = event a diamond is selected. Determine P(B|A).

0.25

The following contingency table provides a joint frequency distribution for the popular votes cast in the presidential election by region and political party. Data are in thousands, rounded to the nearest thousand. A person who voted in the presidential election is selected at random. Compute the probability that the person selected voted Democrat.

0.406

The Book Industry Study Group, Inc., performs sample surveys to obtain information on characteristics of book readers. A book reader is defined to be one who read one or more books in the six months prior to the survey; a non-book reader is defined to be one who read newspapers or magazines but no books in the six months prior to the survey; a nonreader is defined to be one who did not read a book, newspaper, or magazine in the six months prior to the survey. The following data were obtained from a random sample of people 16 years old and over. 131 150 17 298 159 141 11 311 200 98 4 302 663 656 87 1406 Suppose one of these people is selected at random. Compute P( C2 or I2).

0.572

Of the 91 people who answered "yes" to a question, 5 were male. Of the 81 people who answered "no" to the question, 13 were male. If one person is selected at random from the group, what is the probability that the person answered "yes" or was male?

0.605

For a person selected randomly from a certain population, events A and B are defined as follows. A = event the person is male B = event the person is a smoker For this particular population, it is found that P(A) = 0.47, P(B) = 0.29, and P(A & B) = 0.15. Find P(A or B). Round approximations to two decimal places.

0.61

Use a table of areas to find the specified area under the standard normal curve. The area that lies to the left of 1.13

0.8708

Use a table of areas to find the specified area under the standard normal curve. The area that lies either to the left of 1.56 or to the right of 2.30

0.9513

Use a table of areas to find the specified area under the standard normal curve. The area that lies to the right of -1.82

0.9656

Scores on a test have a mean of 70 and a standard deviation of 8. Michelle has a score of 78. Convert Michelle's score to a z-score.

1

Identify potential outliers, if any, for the given data. The National Education Association collects data on the number of years of teaching experience of high-school teachers. A sample taken this year of 19 high-school teachers yielded the following data on number of years of teaching experience. 16 24 1 32 15 6 18 8 20 14 17 19 16 10 21 26 14 38 18

1, 32, 38

Find the specified t-value.For a t-curve with df = 11, find t= 0.10.

1.363

Find the z-score corresponding to the given value and use the z-score to determine whether the value is unusual. Consider a score to be unusual if it is at least three standard deviations above or below the mean. Round the z-score to one decimal place, if necessary. A test score of 88.0 on a test having a mean of 70 and a standard deviation of 10.

1.8; not unusual

The members of a board of directors have the following roles: president (P), vice president (V), secretary (S), treasury (T), and fundraiser (F). Consider these board members to be a population of interest. The possible samples (without replacement) of size two that can be obtained from these five board members are as follows. P,V P,S P,T P,F V,S V,T V,F S,T S,F T,F If a simple random sampling method is used to obtain a sample of two of the board members, what are the chances of selecting the secretary and the treasurer?

1/10

The finalists in an essay competition are Lisa (L), Melina (M), Ben (B), Danny (D), Eric (E), and Joan (J). Consider these finalists to be a population of interest. The possible samples (without replacement) of size two that can be obtained from this population of six finalists are as follows. L,M L,B L,D L,E L,J M,B M,D M,E M,J B,D B,E B,J D,E D,J E,J If a simple random sampling method is used to obtain a sample of two of the finalists, what are the chances of selecting Lisa and Danny?

1/15

The test scores of 40 students are summarized in the frequency distribution below. Find the standard deviation. Score Students 50-under 60: 14 60-under 70: 5 70-under 80: 8 80-under 90: 7 90-under 100: 6

14.9

The mean of a set of data is 116.53 and its standard deviation is 116.22. Find the z-score for a value of 395.29. Round your final answer to two decimal places.

2.4

Find the specified t-value. For a t-curve with df = 20, find t= 0.01.

2.528

A card is drawn from a well-shuffled deck of 52 cards. What is the probability of drawing an ace or a 7?

2/13

Find the median for the given sample data. A store manager kept track of the number of newspapers sold each week over a seven-week period. The results are shown below. 85, 15, 214, 168, 292, 237, 235

214

Identify potential outliers, if any, for the given data. The weekly salaries (in dollars) of 24 randomly selected employees of a company are shown below. 310 320 450 460 470 500 520 540 580 600 650 700 710 840 870 900 1000 1200 1250 1300 1400 1720 2500 3700

2500, 3700

Find the median for the given sample data. The normal monthly precipitation (in inches) for August is listed for 20 different U.S. cities. 3.5 1.6 2.4 3.7 4.1 3.9 1.0 3.6 4.2 3.4 3.7 2.2 1.5 4.2 3.4 2.7 0.4 3.7 2.0 3.6

3.45 in

Identify potential outliers, if any, for the given data. The test scores of 15 students are listed below. 38 41 56 65 66 68 70 72 74 77 78 82 87 90 99

38, 41

The mean of a set of data is 5.87 and its standard deviation is 2.10. Find the z-score for a value of 14.93. Round your final answer to two decimal places.

4.31

Find the sample standard deviation for the given data. Round your final answer to one more decimal place than that used or the observations. 22, 29, 21, 24, 27, 28, 25, 36

4.8

A card is drawn from a well-shuffled deck of 52 cards. What is the probability of drawing a face card or a 5?

4/13

Use the given table to determine the mean, μx, of the variable x for the given sample size. 92) Sample x 3, 4 3.5 3, 5 4 3, 6 4.5 3, 7 5 4, 5 4.5 4, 6 5 4, 7 5.5 5, 6 5.5 5, 7 6 6, 7 6.5

5

The manager of a bank recorded the amount of time each customer spent waiting in line during peak business hours one Monday. The frequency distribution below summarizes the results. Find the standard deviation. Round your answer to one decimal place. Waiting time (minutes) 0-under 4: 14 4-under 8: 14 8-under 12: 12 12-under 16: 8 16-under 20: 0 20-under 24: 2

5.1

Find the indicated probability by using the general addition rule. When two balanced dice are rolled, there are 36 possible outcomes. Find the probability that either doubles are rolled or the sum of the dice is 8.

5/18

A data set has 50 observations and has mean 55 and standard deviation 10. Approximately how many observations lie between 25 and 85?

50

At one college, GPA's have a roughly bell-shaped distribution with a mean of 2.9 and a standard deviation of 0.6. What percentage of students at the college have a GPA between 2.3 and 3.5?

68%

Find Q3. 1, 3, 6, 7, 10, 1, 3, 6, 7, 10

7

Find the conditional probability. In Anne's community college, 42.2% of students are Asian and 3.6% are Asian chemistry majors. What percentage of Asian students are chemistry majors?

8.5%

A lottery game has balls numbered 1 through 19. What is the probability of selecting an even numbered ball or the number 12 ball?

9/19

Which of the following could not possibly be probabilities? A. -0.04 B. 10/7 C. 0 D. 0.20 6

A and B

Given a group of students: Allen (A), Brenda (B), Chad (C), Dorothy (D), and Eric (E), list all of the possible samples (without replacement) of size four that can be obtained from the group. List all possible samples from the specified population.

A,B,C,D A,B,C,E A,C,D,E A,D,E,B B,C,D,E

Three board members for a nonprofit organization will be selected from a group of five people. The board members will be selected by drawing names from a hat. The names of the five possible board members are Allison, Bob, Charlie, Dave, and Emily. The possible outcomes can be represented as follows. ABC ABD ABE ACD ACE ADE BCD BCE BDE CDE Here, for example, ABC represents the outcome that Allison, Bob, and Charlie are selected to be on the board. The events A and B are defined as follows. A = event that Dave is selected B = event that fewer than two men are selected List the outcomes that comprise the event (A & B)

ABD, ADE, BDE

Three board members for a nonprofit organization will be selected from a group of five people. The board members will be selected by drawing names from a hat. The names of the five possible board members are Allison, Bob, Charlie, Dave, and Emily. The possible outcomes can be represented as follows. ABC ABD ABE ACD ACE ADE BCD BCE BDE CDE Here, for example, ABC represents the outcome that Allison, Bob, and Charlie are selected to be on the board. The event A is defined as follows. A = event that Bob and Dave are both selected List the outcomes that comprise the event (not A).

ABC, ABE, ACD, ACE, ADE, BCE, CDE

Geologists have an interest in the structure and the history of the earth. A geologist can go back in time by drilling deep into the ground, retrieving a core sample, estimating the ages of the various layers, and examining the composition. A timeline can be built of the entire area from where the core sample was drilled. A geologist may retrieve several core samples to confirm the history of the earth's structure in that sampled area. Mountains, lakes, and unstable ground can easily impede a simple random sampling of a desired geographical area, therefore what is the most realistic sampling method that represents the actual drillings, comparisons, and scientific examinations of several core samples within the same geographical area?

Cluster sampling

An education researcher was interested in examining the effect of the teaching method and the effect of the particular teacher on students' scores on a reading test. In a study, there are two different teachers (Juliana and Felix) and three different teaching methods (method A, method B, and method C). The number of students participating in the study is 258. Students are randomly assigned to a teaching method and teacher. Identify the treatments.

Juliana and method A, Juliana and method B, Juliana and method C, Felix and method A, Felix and method B, Felix and method C

Determine the null and alternative hypotheses for the proposed hypothesis test. A researcher wants to perform a hypothesis test to determine whether the mean length of marriages in California differs from the mean length of marriages in Texas.

Let μ1 denote the mean length of marriages in California and let μ2 denote the mean length of marriages in Texas. The null and alternative hypotheses are H0: μ1 = μ2 and Ha: μ1 =/ μ2

The National Weather Service keeps records of snowfall in mountain ranges. Records indicate that in a certain range, the annual snowfall has a mean of 82 inches and a standard deviation of 12 inches. Suppose the snowfalls are sampled during randomly picked years. For samples of size 36, determine the mean and standard deviation of x.

ux= 82, st. dev. x= 2

The members of a board of directors have the following roles: president (P), vice president (V), secretary (S), treasury (T), and fundraiser (F). Consider these board members to be a population of interest. List the 10 possible samples (without replacement) of size two from this population of five board members. List all possible samples from the specified population.

P,V P,S P,T P,F V,S V,T V,F S,T S,F T,F

In a clinical trial, 780 participants suffering from high blood pressure were randomly assigned to one of three groups. Over a one-month period, the first group received a low dosage of an experimental drug, the second group received a high dosage of the drug, and the third group received a placebo. The diastolic blood pressure of each participant was measured at the beginning and at the end of the period and the change in blood pressure was recorded. Identify the levels of the factor.

Placebo, low dosage, high dosage

After training intensively for six months, John hopes that his mean time to run 100 meters has decreased from last year's mean time of 11.9 seconds. He performs a hypothesis test to determine whether his mean time has decreased. Preliminary data analyses indicate that it is reasonable to apply a z-test. The hypotheses are H 0: μ = 11.9 seconds H a: μ < 11.9 seconds. Assume that Η = 0.33 seconds, n = 26, and the significance level is 0.10. Express the decision criterion for the hypothesis test in terms of x.

Reject H 0 if x < 11.82 seconds

A z-test is to be performed for a population mean. Express the decision criterion for the hypothesis test in terms of x. That is, determine for what values of x the null hypothesis would be rejected. 107) A hypothesis test is to be performed to determine whether the mean waiting time during peak hours for customers in a supermarket has increased from the previous mean waiting time of 8.9 minutes. Preliminary data analyses indicate that it is reasonable to apply a z-test. The hypotheses are H 0: μ = 8.9 minutes Ha: μ > 8.9 minutes. The population standard deviation is 3.3 minutes. The sample size is 34. The significance level is 0.05. Express the decision criterion for the hypothesis test in terms of x

Reject H 0 if x > 9.83 minutes

Find the range and standard deviation for each of the two samples, then compare the two sets of results. When investigating times required for drive-through service, the following results (in seconds) were obtained. Restaurant A 120 67 89 97 124 68 72 96 Restaurant B 115 126 49 56 98 76 78 95

Restaurant A: 57; 22.2 Restaurant B: 77; 27.0 Both measures indicate there is more variation in the data for restaurant B than the data for restaurant A.

An employee at the local ice cream parlor asks three customers if they like chocolate ice cream. Identify the sample and population.

Sample: the 3 selected customers; population: all customers

In a poll of 50,000 randomly selected college students, 74% answered "yes" when asked "Do you have a television in your dorm room?" Identify the sample and population.

Sample: the 50,000 selected college students; population: all college students

An education researcher was interested in examining the effect of the teaching method and the effect of the particular teacher on students' scores on a reading test. In a study, there are four different teachers (Juliana, Felix, Sonia, and Helen) and three different teaching methods (method A, method B, and method C). The number of students participating in the study is 258. Students are randomly assigned to a teaching method and teacher. Identify the response variable.

Score on reading test

x = 137, s = 14.2, n = 20, H0: μ = 132, Ha: mean=/ 132, sig. level= 0.1

Test statistic: t = 1.57. P-value = 0.1318. Do not reject H0. There is not sufficient evidence to conclude that the mean is different from 132. The evidence against the null hypothesis is weak or none.

x = 84.5, s = 11.2, n = 16, H0: μ = 80, Ha: μ < 80, sig. level= 0.01.

Test statistic: t = 1.61. P-value = 0.9356. Do not reject the null hypothesis. There is not sufficient evidence to conclude that the mean is less than 80. The evidence against the null hypothesis is weak or none.

A herpetologist performed a study on the effects of the body type and mating call of the male bullfrog as signals of quality to mates. Four life-sized dummies of male bullfrogs and two sound recordings provided a tool for testing female response to the unfamiliar frogs whose bodies varied by size (large or small) and color (dark or light) and whose mating calls varied by pitch (high, normal, or low). The female bullfrogs were observed to see whether they approached each of the four life-sized dummies. Identify the experimental units.

The female bullfrogs

A designed experiment is described. Identify the specified element of the experiment. In a clinical trial, 780 participants suffering from high blood pressure were randomly assigned to one of three groups. Over a one-month period, the first group received a low dosage of an experimental drug, the second group received a high dosage of the drug, and the third group received a placebo. The diastolic blood pressure of each participant was measured at the beginning and at the end of the period and the change in blood pressure was recorded. Identify the experimental units (subjects).

The participants in the experiment

A confidence interval (CI) for the difference μ1 - μ2 between two population means is given. Interpret the confidence interval. 90% CI from -30 to 230

We can be 90% confident that μ1 - μ2 lies somewhere between -30 and 230. Equivalently, we can be 90% confident that μ1 is somewhere between 30 less than and 230 more than μ2.

Which is better, a score of 92 on a test with a mean of 71 and a standard deviation of 15, or a score of 688 on a test with a mean of 493 and a standard deviation of 150? (Assume that the distributions being compared have approximately the same shape.)

a score of 92

43% of the murder trials in one district result in a guilty verdict. Five murder trials are selected at random from the district. Determine the probability distribution of X, the number of trials among the five selected in which the defendant is found guilty.

x P(X = x) 0 0.0602 1 0.2270 2 0.3424 3 0.2583 4 0.0975

The mean annual income for adult women in one city is $28,520 and the standard deviation of the incomes is $5100. The distribution of incomes is skewed to the right. Determine the sampling distribution of the mean for samples of size 71.

approximately normal, mean=$28,520, standard deviation =$605

Which score has a higher relative position, a score of 34.8 on a test with a mean of 25 and a standard deviation of 7, or a score of 257.4 on a test with a mean of 214 and a standard deviation of 31?(Assume that the distributions being compared have approximately the same shape.)

both scores have the same relative position

In a clinical trial, 780 participants suffering from high blood pressure were randomly assigned to one of three groups. Over a one-month period, the first group received a low dosage of an experimental drug, the second group received a high dosage of the drug, and the third group received a placebo. The diastolic blood pressure of each participant was measured at the beginning and at the end of the period and the change in blood pressure was recorded. Identify the response variable.

change in diastolic blood pressure

400 patients suffering from chronic back pain were randomly assigned to one of two groups. Over a four-month period, the first group received acupuncture treatments and the second group received a placebo. Patients who received acupuncture treatments improved more than those who received the placebo. Identify as observational study or designed experiment.

designed experiment

A researcher wished to assess the importance of exercise in weight-loss programs. 412 people, all considered to be at least 20 pounds overweight, volunteered to participate in a study. The participants were randomly assigned to one of two groups. Over a two-month period, the first group followed a particular diet but were instructed to perform no exercise other than walking.The second group followed the same diet but also performed aerobic exercise for one hour each day. At the end of the two months, the weight loss of each participant was recorded. The average weight loss was calculated for each group and it was found that the average weight loss for the second group was significantly greater than the average weight loss for the first group. Identify as observational study or designed experiment.

designed experiment

The significance level and P-value of a hypothesis test are given. Decide whether the null hypothesis should be rejected. sig. level = 0.05, P-value = 0.058

do not reject

The spell-checker in a desktop publishing application may not catch all misspellings (e.g. their, there) or correctly interpret the spellings of proper names. Jackie is an expert editor and can proofread extremely quickly. Jackie is hired by a book publisher to check the spelling of every word in the latest proof of a history book. With regard to Jackie's assignment, what is the population?

every word in the latest proof of the history book

An experiment consists of randomly selecting a card from a deck of 52. Three events A, B, and C are defined for this experiment. True or false, if no outcome is common to the three events then the events are mutually exclusive?

false

True or false, if the events A and B are mutually exclusive and the events B and C are mutually exclusive, then the collection of events A, B, and C must be mutually exclusive?

false

When a balanced die is rolled, the probability that the number that comes up will be a one is 1/6. This means that if the die is rolled 36 times, a one will show up six times.

false

The age distribution of students at a community college is given below. Age (years) Number of students (f) Under 21 2890 21-24: 2190 25-28: 1276 29-32: 651 33-36: 274 37-40: 117 Over 40: 185 A student from the community college is selected at random. The events A, B, and C are defined as follows. A = event the student is at most 28 B = event the student is at least 33 C = event the student is between 21 and 24 inclusive Is the collection of events A, B, and C mutually exclusive?

no

The weights of people in a certain population are normally distributed with a mean of 154 lb and a standard deviation of 23 lb. Determine the sampling distribution of the mean for samples of size 4.

normal, mean= 154 lb, standard deviation= 11.5 lb

A political pollster reports that his candidate has a 10% lead in the polls with 10% undecided. Identify as observational study or designed experiment.

observational study

An educational researcher used school records to determine that, in one school district, 84% of children living in two-parent homes graduated high school while 75% of children living in single-parent homes graduated high school. Identify as observational study or designed experiment.

observational study

At one hospital in 1992, 674 women were diagnosed with breast cancer. Five years later, 88% of the Caucasian women and 83% of the African American women were still alive. Identify as observational study or designed experiment.

observational study

A magazine publisher mails a survey to every subscriber asking about the quality of its subscription service. The total number os subscribers represents what?

population

The significance level and P-value of a hypothesis test are given. Decide whether the null hypothesis should be rejected. sig. level = 0.10, P-value = 0.08

reject

The significance level and P-value of a hypothesis test are given. Decide whether the null hypothesis should be rejected. sig. level= 0.05, P-value = 0.017

reject

A pollster uses a computer to generate 500 random numbers and then interviews the voters corresponding to those numbers. Identify the type of sampling used in this example.

simple random sampling

A mega-discount chain store just opened a new clothing store in town emphasizing mainly women's clothing. Before opening, management had to decide whether to only carry either men's, women's, boys', girls', or infants' clothing. After performing representative sampling of potential customers from each of these groups, it was decided to carry only women's clothing. Identify the type of sampling used in this example.

stratified sampling

At a college there are 120 freshmen, 90 sophomores, 110 juniors, and 80 seniors. A school administrator selects a simple random sample of 12 of the freshmen, a simple random sample of 9 of the sophomores, a simple random sample of 11 of the juniors, and a simple random sample of 8 of the seniors. She then interviews all the students selected. Identify the type of sampling used in this example.

stratified sampling

From a group of 496 students, every 49th student starting with the 3rd student is selected. Identify the type of sampling used in this example.

systematic random sampling

A computer network manager wants to test the reliability of some new and expensive fiber-optic Ethernet cables that computer department just received. The computer department received 4 boxes containing 50 cables each. The manager does not have the time to test every cable in each box. The manager will choose one box at random and test 10 cables chosen randomly within that box. What is the sample?

the 10 cables chosen for testing

True or false? In simple random sampling, each possible sample is equally likely to be the one obtained.

true

The mean and the standard deviation of the sampled population are, respectively, 125.4 and 24.1. n = 49

ux= 125.4, st. dev. x= 3.4

multiple choice test consists of four questions. Each question has five possible answers of which only one is correct. A student guesses on every question. Find the probability distribution of X, the number of questions she answers correctly.

x P(X = x) 0 0.4096 1 0.4096 2 0.1536 3 0.0256 4 0.0016

Three board members for a nonprofit organization will be selected from a group of five people. The board members will be selected by drawing names from a hat. The names of the five possible board members are Allison, Betty, Charlie, Dave, and Emily. The possible outcomes can be represented as follows. ABC ABD ABE ACD ACE ADE BCD BCE BDE CDE Here, for example, ABC represents the outcome that Allison, Betty, and Charlie are selected to be on the board. The events A and B are defined as follows. A = event that Betty and Allison are both selected B = event that more than one man is selected Are the events A and B mutually exclusive?

yes

A variable x has a mean, μ, of 27 and a standard deviation, Η, of 2. Determine the standardized version of x.

z = x - 27/ 2