Psych Stat Exam 2

standardized distribution

-An entire distribution that has been transformed to create predetermined values for μ and σ. - composed of scores that have been transformed to crate predetermined value for μ and s.

standardized score

A score that has been transformed into a standard form.

raw score

An original, untransformed observation or measurement.

deviation score

The distance (and direction) from the mean to a specific score.

The distribution of IQ scores is normal with a mean of μ = 100 and a standard deviation of σ = 15. What proportion of the population have IQ scores greater than 105? a. 0.3707 b. 0.1293 c. 0.3333 d. 0.6293

a. 0.3707

For a normal distribution with μ = 90 and σ = 5, what is the probability of selecting a score less than X = 84? a. 11.51% b. 88.49% c. 54% d. 38.49%

a. 11.51%

Scores on the SAT form a normal distribution with a mean of μ = 500 and σ = 100. In this distribution, what is the probability of randomly selecting a score less than X = 450? a. 30.85% b. 80.85% c. 69.15% d. 19.15%

a. 30.85%

For any normal distribution, what is the probability of selecting a score less than the mean? a. 50% b. Cannot be determined without additional information c. 25% d. 34.13%

a. 50%

For a normal distribution with μ = 500 and σ = 100, what score separates the bottom 60% of the distribution from the rest? a. 475 b. 584 c. 525 d. 552

c. 525

Scores on the SAT form a normal distribution with μ = 500 and σ = 100. What is the minimum SAT score needed to be in the top 10% of the distribution? a. X = 590 b. X = 525 c. X = 628 d. X = 733

c. X = 628

For a normal distribution with μ = 100 and σ = 10, what scores (X values) separate the middle 95% from the rest? a. X = 83.5 and X = 116.5 b. X = 87.2 and X = 112.8 c. X = 80.4 and X = 119.6 d. X = 95 and X = 105

c. X = 80.4 and X = 119.6

SAT scores form a normal distribution with a mean of μ = 500 and a standard deviation of σ = 100. What scores form the boundaries for the middle 50% of the distribution? a. 400 and 600 b. 450 and 550 c. 304 and 696 d. 433 and 567

d. 433 and 567

For a normal distribution with μ = 500 and σ = 100, what score separates the top 60% of the distribution from the rest? a. 525 b. 584 c. 552 d. 475

d. 475

A distribution is normal and has μ = 90 and σ = 10. What score separates the bottom 64% of the distribution from the rest? a. 96.4 b. 91.4 c. 104 d. 93.6

d. 93.6

For any distribution the score that separates the highest 10% from the rest of the scores, is called _____. a. the 10th percentile b. the 40th percentile c. the 60th percentile d. the 90th percentile

d. the 90th percentile

observation stats

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For a population with σ = 4, an individual with a deviation score of +2 would have a z-score of _____. a. +2.00 b. +8.00 c. Cannot be determined without knowing the population mean d. +0.50

d. +0.50

In a distribution with μ = 60 and σ = 10 a score of X = 45 is below the mean by exactly 1.50 standard deviations, which means that it corresponds to a z-score of z = −1.50. For this same distribution, what is the z-score corresponding to X = 70? a. z = +1.00 b. z = +2.50 c. z = +0.50 d. z = +0.25

a. z = +1.00

What proportion of a normal distribution is located between z = 1.00 and z = 1.50? a. 0.0919 b. 0.5000 c. 0.7745 d. 0.2255

a. 0.0919

A normal distribution has a mean of µ = 500 with σ = 100. Given that 15.87% of the distribution is located in the tail beyond z = 1.00, what is the probability of selecting an individual with a score less than 400? a. 0.1587 b. 0.8413 c. −0.15.87 d. 0.34.13

a. 0.1587

The proportion of a normal distribution that corresponds to values less than z = 1.00 is p = 0.8413. Base on this information, what is the proportion that corresponds to values less than z = −1.00? a. 0.1587 b. −0.1587 c. 0.8413 d. −0.8413

a. 0.1587

A vertical line is drawn through a normal distribution at z = 1.00. The proportion of the distribution that is located between the mean and the line is ________. a. 0.3413 b. 0.6826 c. 0.1587 d. 0.8413

a. 0.3413

A normal distribution has a mean of μ = 36 with σ = 4. What proportion of the distribution is located between scores of X = 30 and X = 38? a. 0.6247 b. 0.3753 c. 0.7417 d. 0.2583

a. 0.6247

A jar contains 10 red marbles and 40 black marbles. If one marble is selected from this jar, what is the probability that the marble will be red? a. 10/50 b. 1/50 c. 1/40 d. 10/40

a. 10/50

SAT scores for a normal distribution with mean of µ = 500 with σ = 100. Given that a z-score that is greater than or equal to 1.28 is needed to be in the top 10% of a normal distribution, that what SAT scores form the boundaries for the middle 80% of the distribution? a. 372 and 628 b. 128 and 528 c. 428 and 428 d. 498.72 and 501.28

a. 372 and 628

For a population with μ = 60 and σ = 8, what is the X value corresponding to z = −0.50? a. 56 b. -4 c. 59.5 d. 64

a. 56

A vertical like is drawn through a normal distribution at z = +0.25. How much of the distribution is on the left-hand side? a. 59.87% b. 75% c. 25% d. 40.13%

a. 59.87%

For any normal distribution, what is the percentile rank for z = 0.50? a. 69.15% b. 30.85% c. 51.99% d. 48.01%

a. 69.15%

A colony of laboratory rats contains 7 albino rats and 23 hooded rats. What is the probability of randomly selecting an albino rat from this colony? a. 7/30 b. 23/7 c. 7/23 d. 23/30

a. 7/30

A population of scores has σ = 10. In this population, a score of X = 60 corresponds to z = −1.50. What is the population mean? a. 75 b. 90 c. 45 d. −30

a. 75

A vertical line is drawn through a normal distribution at z = −1.00. The line separates the distribution into two sections and the larger section corresponds to ________ of the whole distribution. a. 84.13% b. −84.13% c. 99% d. 75%

a. 84.13%

For a population with µ = 100 and σ = 20, what is the X value corresponding to z = −0.25? a. 95 b. 99.75 c. 92.5 d. 97.5

a. 95

In a sample with s = 8, a score of X = 44 corresponds to a z-score of z = −0.50. What is the sample mean? a. M = 48 b. M = 52 c. M = 40 d. M = 36

a. M = 48

Last week Sarah had exams in Math and in Spanish. On the Math exam, the mean was μ = 30 with σ = 5, and Sarah had a score of X = 45. On the Spanish exam, the mean was μ = 60 with σ = 6 and Sarah had a score of X = 65. For which class should Sara expect the better grade? a. Math b. Spanish c. The grades should be the same because the two exam scores are in the same location. d. There is not enough information to determine which is the better grade.

a. Math

A population distribution has μ = 80 and σ = 6. In this distribution a z-score of z = +2.00 identifies a location ________. a. twelve points above the mean b. two points below the mean c. twelve points below the mean d. two points above the mean

a. twelve points above the mean

Of the following z-score values, which one represents the location closest to the mean? a. z = +0.50 b. z = +1.00 c. z = −1.00 d. z = −2.00

a. z = +0.50

z-score transformation

changing raw scores into z-scores

In a sample with a mean of M = 45 and a standard deviation of s = 5, a z-score of z = −2 corresponds to X = 35 because the score is below the mean by exactly 2 standard deviations. What is the z-score corresponding to X = 40? a. z = −1.00 b. z = +1.00 c. z = −5.00 d. z = −0.50

a. z = −1.00

A population with µ = 85 and σ = 12 is transformed into z-scores. After the transformation, the population of z-scores will have a mean of _____. a. µ = 0 b. Cannot be determined from the information given c. µ = 1.00 d. µ = 85

a. µ = 0

If your exam score is X = 60, which set of parameters would give you the best grade? a. μ = 50 and σ = 5 b. μ = 55 and σ = 5 c. μ = 50 and σ = 10 d. μ = 55 and σ = 10

a. μ = 50 and σ = 5

For a population with µ = 80 and σ = 10, what is the z score corresponding to X = 85? a. +1.00 b. +0.50 c. +2.00 d. +5.00

b. +0.50

The mean for any distribution corresponds to a z score of ________. a. 1 b. 0 c. Cannot be determined from the information given d. N

b. 0

A normal distribution has a mean of µ = 40 with σ = 4. Given that 6.68% of the distribution is located in the tail beyond z = 1.50, what is the probability of selecting an individual with a score greater than 46? a. 0.4452 b. 0.0668 c. 0.0548 d. 0.9332

b. 0.0668

For a normal distribution, the proportion in the tail beyond z = 1.50 is p = 0.0668. Based on this information, what is the proportion in the tail beyond z = −1.50? a. −0.0668 b. 0.0668 c. 0.9332 d. −0.9332

b. 0.0668

What proportion of a normal distribution is located in the tail beyond a z-score of z = −1.50? a. −0.9332 b. 0.0668 c. 0.9332 d. −0.0668

b. 0.0668

What proportion of a normal distribution corresponds to z scores greater than +1.04? a. 0.6492 b. 0.1492 c. 0.8508 d. 0.3508

b. 0.1492

A vertical line is drawn through a normal distribution at z = −0.50. What proportion of the distribution is located between the mean and the line? a. −0.3085 b. 0.1915 c. −0.1915 d. 0.3085

b. 0.1915

What proportion of a normal distribution falls between z = −1.16 and z = +1.16? a. 0.3770 b. 0.7540 c. 0.6230 d. 0.2460

b. 0.7540

An introductory psychology class has 9 freshman males, 15 freshman females, 8 sophomore males, and 12 sophomore females. If a random sample of n = 3 students is selected and the first two are both females, then, what is the probability that the third student is a male? a. 17/20 b. 17/44 c. 8/20 d. 9/24

b. 17/44

An introductory psychology class has 9 freshman males, 15 freshman females, 8 sophomore males, and 12 sophomore females. What is the probability of randomly selecting a male from this group? a. 17/20 b. 17/44 c. 8/20 d. 9/24

b. 17/44

A vertical line is drawn through a normal distribution at z = −1.00 and 84.13% of the distribution is on the right-hand side of the line. How much of the distribution is located between the line and the mean? a. 15.87% b. 34.13% c. 84.13% d. −15.87%

b. 34.13%

A population of scores has μ = 50. In this population, an X value of 58 corresponds to z = 2.00. What is the population standard deviation? a. 2 b. 4 c. 8 d. 16

b. 4

SAT scores for a normal distribution with mean of µ = 500 with σ = 100. Given that a z-score that is greater than or equal to 1.28 is needed to be in the top 10% of a normal distribution, that what SAT score separates the top 10% from the rest? a. 128 b. 628 c. 501.28 d. 372

b. 628

For a population with µ = 60 and σ = 8, what is the X value corresponding to z = 1.50? a. 90 b. 72 c. 61.5 d. 12

b. 72

A population of scores has μ = 44. In this population, an X value of 40 corresponds to z = −0.50. What is the population standard deviation? a. 4 b. 8 c. 6 d. 2

b. 8

Probability values are always _____. a. greater than or equal to 0 b. All of the other 3 choices are correct. c. less than or equal to 1 d. positive numbers

b. All of the other 3 choices are correct.

Which of the following is (are) required for a random sample? a. There must be sampling with replacement. b. All of the other 3 choices are correct. c. The probabilities cannot change during a series of selections. d. Every individual has an equal chance of being selected.

b. All of the other 3 choices are correct.

For a sample with a mean of M = 70, what is the z-score corresponding to a score that is located 10 points below the mean? a. −10 b. Cannot answer without knowing the standard deviation c. +1 d. −1

b. Cannot answer without knowing the standard deviation

For a symmetrical population with μ = 100 the z score corresponding to X = 120 would be ________. a. 2.00 b. Cannot be determined from the information given c. 1.20 d. 1.00

b. Cannot be determined from the information given

For a normal distribution with μ = 60 with σ = 8, what is the probability of selecting a score greater than X = 64? a. It is equal to the proportion of the distribution with z-scores greater than 1.00. b. It is equal to the proportion of the distribution with z-scores greater than 0.50. c. It is equal to the proportion of the distribution with z-scores greater than 4.00. d. It is equal to the proportion of the distribution with z-scores greater than 2.00.

b. It is equal to the proportion of the distribution with z-scores greater than 0.50.

Last week Sarah had exams in Math and in Spanish. She had a score of 45 on the Math exam and a score of 65 on the Spanish exam. For which class should Sara expect the better grade? a. Spanish b. There is not enough information to determine which is the better grade. c. The grades should be the same because the two exam scores are in the same location. d. Math

b. There is not enough information to determine which is the better grade.

For the past 20 years, the high temperature on April 15th has averaged µ = 62 degrees with a standard deviation of σ= 8. Last year, the high temperature was 66 degrees. Based on this information, last year's temperature on April 15th was _____. a. above average, but it is impossible to describe how much above average b. a little above average c. There is not enough information to compare last year with the average. d. far above average

b. a little above average

A location that is above the mean by one half of a standard deviation is assigned a z-score of z = +0.50. What z-score is assigned to a location that is below the mean by one standard deviation? a. z = +2.00 b. z = −1.00 c. z = −2.00 d. z = +1.00

b. z = −1.00

For a normal distribution, z = 1.28 separates the highest 10% of the distribution from the lowest 90%. What z-score separates the lowest 10% of the distribution from the rest? a. z = −0.90 b. z = −1.28 c. z = 1.28 d. z = 0.90

b. z = −1.28

If your exam score is X = 60, which set of parameters would give you the best grade? a. μ = 70 and σ = 2 b. μ = 65 and σ = 5 c. μ = 70 and σ = 5 d. μ = 65 and σ = 2

b. μ = 65 and σ = 5

A population with μ = 85 and σ = 12 is transformed into z-scores. After the transformation, the population of z-scores will have a standard deviation of ________. a. σ = 12 b. σ = 1.00 c. Cannot be determined from the information given d. σ = 0

b. σ = 1.00

For a distribution of exam scores with μ = 50, which value for the standard deviation would give the highest grade to a score of X = 45? a. σ = 2 b. σ = 10 c. σ = 1 d. σ = 5

b. σ = 10

For a population with μ = 100 and σ = 20, what is the z-score corresponding to X = 105? a. +5.00 b. +0.50 c. +0.25 d. +4.00

c. +0.25

What proportion of the scores in a normal distribution have z-scores less than z = −1.32? a. 0.9066 b. 0.4066 c. 0.0934 d. 0.5934

c. 0.0934

What proportion of the scores in a normal distribution have z-scores less than z = 0.86? a. 0.6949 b. 0.1949 c. 0.8051 d. 0.3051

c. 0.8051

A jar contains 40 red marbles and 10 black marbles. If you take a random sample of n = 3 marbles from this jar, and the first two marbles are both red, what is the probability that the third marble will be black? a. 9/49 b. 10/49 c. 10/50 d. either 9/49 or 10/49

c. 10/50

What proportion of a normal distribution is located in the tail beyond z = 2.00? a. 2% b. 97.72% c. 2.28% d. 1.14%

c. 2.28%

Exactly 95% of a normal distribution is located between z = +1.96 and z = −1.96. How much of the distribution is located in the tail beyond z = +1.96? a. 90% b. 5% c. 2.5% d. 10%

c. 2.5%

A population of scores has µ = 42. In this population, an X value of 40 corresponds to z = −0.50. What is the population standard deviation? a. 2 b. −2 c. 4 d. −4

c. 4

For a normal distribution with µ = 100 and σ = 10, what is the probability of selecting a score less than X = 85? a. -6.68% b. 43.32% c. 6.68% d. 93.32%

c. 6.68%

A population of scores has σ= 20. In this population, a score of X = 80 corresponds to z = +0.25. What is the population mean? a. 85 b. 90 c. 75 d. 70

c. 75

Last week Tom had exams in Statistics and in English. He scored 10 points above the mean on both exams. From this information, you can conclude: a. Tom has identical z-scores for the two exams. b. Tom will have a higher z-score for the exam with the lower mean. c. Both of Tom's z-scores are positive. d. None of the other choices is correct

c. Both of Tom's z-scores are positive.

Random sampling requires sampling with replacement. What is the goal of sampling with replacement? a. It ensures that every individual has an equal chance of selection. b. All of the other options are goals of sampling with replacement. c. It ensures that the probabilities stay constant from one selection to the next. d. It ensures that the same individual is not selected twice.

c. It ensures that the probabilities stay constant from one selection to the next.

Which of the following is an advantage of transforming X values into z scores? a. All scores are moved closer to the mean. b. The distribution is transformed to a normal shape. c. None of the other options is an advantage. d. All negative numbers are eliminated.

c. None of the other options is an advantage.

Last week Sarah had exams in Math and in Spanish. On the Math exam, the mean was μ = 40 with σ = 5, and Sarah had a score of X = 45. On the Spanish exam, the mean was μ = 60 with σ = 8 and Sarah had a score of X = 68. For which class should Sara expect the better grade? a. Math b. There is not enough information to determine which is the better grade. c. The grades should be the same because the two exam scores are in the same location. d. Spanish

c. The grades should be the same because the two exam scores are in the same location.

For a sample with M = 100 and s = 10, what is the score corresponding to z = 1.50? a. X = 105 b. X = 101.5 c. X = 115 d. X = 110.5

c. X = 115

A distribution with μ = 35 and σ = 8 is being standardized so that the new mean and standard deviation will be μ = 50 and σ = 10. In the new, standardized distribution your score is X = 60. What was your score in the original distribution? a. X = 45 b. Impossible to determine without more information c. X = 43 d. X = 1.00

c. X = 43

A z-score of z = −2.00 indicates a position in a distribution that is below the mean by a distance equal to 2 standard deviations. What position is indicated by a z-score of z = +1.00? a. above the mean by 1 point b. below the mean by 1 point c. above the mean by a distance equal to 1 standard deviation d. below the mean by a distance equal to 1 standard deviation

c. above the mean by a distance equal to 1 standard deviation

In a sample with M = 60 and s = 10 a score of X = 70 corresponds to a z-score of z = +1.00 because it is above the mean by exactly 1 standard deviation. For this same distribution, what is the z-score corresponding to X = 65? a. z = −0.50 b. z = +0.25 c. z = +0.50 d. z = +1.00

c. z = +0.50

A population has a standard deviation of σ = 8. In this distribution, a score that is 12 points above the mean would correspond to a z-score of ________. a. z = 12.00 b. z = 2.00 c. z = 1.50 d. z = 1.00

c. z = 1.50

In a normal distribution, what z-score value separates the lowest 10% of the scores from the rest of the distribution? a. z = .25 b. z = −.25 c. z = −1.28 d. z = 1.28

c. z = −1.28

For a population with μ = 80 and σ = 10, what is the z score corresponding to X = 70? a. +10 b. −10 c. −1.00 d. +1.00

c. −1.00

A population has μ = 50 and σ = 10. If these scores are transformed into z scores, the population of z scores will have a mean of ________ and a standard deviation of ________. a. 0 and 10 b. 50 and 10 c. 50 and 1 d. 0 and 1

d. 0 and 1

If a sample with M = 60 and s = 8 is transformed into z-scores, then the resulting distribution of z-scores will have a mean of ________ and a standard deviation of ________. a. 60 and 8 (unchanged) b. 60 and 1 c. 0 and 8 d. 0 and 1

d. 0 and 1

What proportion of a normal distribution is located in the tail beyond a z-score of z = −1.50? a. 0.9332 b. −0.0668 c. −0.9332 d. 0.0668

d. 0.0668

For a sample with M = 60 and s = 8, what is the z-score corresponding to X = 62? a. 4 b. 0.50 c. 2 d. 0.25

d. 0.25

A normal distribution has a mean of µ = 60 with σ = 8. Given that 22.66% of the scores in the distribution are greater than X = 66, then what is the probability of selecting an individual with a score greater than 54? a. 0.2266 b. 0.2734 c. 0.7266 d. 0.7734

d. 0.7734

For a normal distribution, which of the following percentiles is located farthest from the mean? a. 75th percentile b. 40th percentile c. 93rd percentile d. 3rd percentile

d. 3rd percentile

In a sample with M = 60, a score of X = 58 corresponds to a z-score of z = −0.50. What is the sample standard deviation? a. 2 b. Cannot be determined without additional information c. 1 d. 4

d. 4

A distribution with µ = 35 and σ = 8 is being standardized so that the new mean and standard deviation will be µ = 50 and σ = 10. When the distribution is standardized, what value will be obtained for a score of X = 39 from the original distribution? a. Impossible to determine without more information b. X = 54 c. X = 1.10 d. X = 55

d. X = 55

In N = 25 games last season, the college basketball team averaged μ = 74 points with a standard deviation of σ = 6. In their final game of the season, the team scored 90 points. Based on this information, the number of points scored in the final game was ________. a. above average, but it is impossible to describe how much above average b. There is not enough information to compare last year with the average. c. a little above average d. far above average

d. far above average

Using z scores, a population with μ = 37 and σ = 6 is standardized so that the new mean is μ = 50 and σ = 10. How does an individual's z score in the new distribution compare with his/her z score in the original population? a. Cannot be determined with the information given b. new z = (10/6)(old z) c. new z = old z + 13 d. new z = old z

d. new z = old z

Under what circumstances would a score that is 15 points above the mean be considered to be near the center of the distribution? a. when the population mean is much larger than 15 b. when the population standard deviation is much smaller than 15 c. when the population mean is much smaller than 15 d. when the population standard deviation is much larger than 15

d. when the population standard deviation is much larger than 15

Under what circumstances would a score that is 15 points above the mean be considered an extreme score? a. when the population mean is much smaller than 15 b. when the population mean is much larger than 15 c. when the population standard deviation is much larger than 15 d. when the population standard deviation is much smaller than 15

d. when the population standard deviation is much smaller than 15

In a distribution with μ = 60 and σ = 10 a score of X = 80 corresponds to a z-score of z = +2.00 because it is above the mean by exactly 2 standard deviations. For this same distribution, what is the z-score corresponding to X = 65? a. z = +1.00 b. z = +0.25 c. z = −0.50 d. z = +0.50

d. z = +0.50

In a normal distribution, what z-score value separates the highest 20% of the scores from the rest of the distribution? a. z = −0.84 b. z = 2.05 c. z = 0.20 d. z = 0.84

d. z = 0.84

For any normal distribution, what z-score value separates the lowest 40% of the distribution from the highest 60%? a. z = −1.28 b. z = 1.28 c. z = 0.25 d. z = −0.25

d. z = −0.25

For a normal distribution, what z-score value separates the lowest 20% of the distribution from the highest 80%? a. z = 0.20 b. z = 0.84 c. z = 0.80 d. z = −0.84

d. z = −0.84

Of the following z-score values, which one represents the most extreme location on the left-hand side of the distribution? a. z = +1.00 b. z = −1.00 c. z = +2.00 d. z = −2.00

d. z = −2.00

For a distribution of exam scores with μ = 70, which value for the standard deviation would give the highest grade to a score of X = 75? a. σ = 2 b. σ = 5 c. σ = 10 d. σ = 1

d. σ = 1

For a sample with a standard deviation of s = 5, what is the z-score corresponding to a score that is located 10 points below the mean? a. +2 b. −10 c. Cannot answer without knowing the mean d. −2

d. −2

simple random sample

group selected from a population, wherein each individual has an equal chance of being selected

z-score

numerical value equal to the distance form the mean measured in standard deviations

random sampling

process of group election, wherein the probability of being selected is constant across individual

propability

the likelihood that a specific event will occur