PSYC 3301 Quiz 4

What z-score corresponds to a score that is above the mean by 2 standard deviations?

+2

For a population with µ = 80 and σ = 6, what is the z-score corresponding to X = 68?

-2.00

If an entire population with μ = 60 and σ = 8 is transformed into z-scores, then the distribution of z-scores will have a mean of ___ and a standard deviation of ___.

0 ; 1

A population distribution has σ = 6. What position in this distribution is identified by a z-score of z = +2.00?

12 points above the mean

A population of scores has µ = 44. In this population, a score of X = 40 corresponds to z = -0.50. What is the population standard deviation?

8

For a population with μ = 34, a score of X = 31 corresponds to z = -1.00. The standard deviation for the population is σ = 6.

False

For a sample with a standard deviation of s = 8, a score of X = 42 corresponds to z = -0.25. The mean for the sample is M = 40.

False

In a population with σ = 4, a score of X = 48 corresponds to z = 1.50. The mean for this population is µ = 42.

True

On an exam, Tom scored 12 points above the mean and had a z-score of +2.00. The standard deviation for the set of exam scores must be σ = 6.

True

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 = 45. What was your score in the original distribution?

X=31

For a population with a standard deviation of σ = 10, what is the z-score corresponding to a score that is 5 points below the mean?

z= -0.50

In a population of scores, X = 44 corresponds to z = +0.50 and X = 50 corresponds to z = +2.00. What are the values for the population mean and standard deviation?

μ = 42 and σ = 4

You have a score of X = 65 on an exam. Which set of parameters would give you the best grade on the exam?

μ = 60 and σ = 5

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 = 8, and Sarah had a score of X = 68. For which class should Sara expect the better grade?

ANSWER: Math STEPS: Find z-score for all classes. Math: (45-30)/5= 3 Spanish: (68-60)/8 = 1

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?

ANSWER: The grades should be the same because the two exam scores are in the same location STEPS: Find z-score for all classes. Math: (45-40)/5=1 Spanish: (68-60)/8=1

In a population of scores, X = 83 corresponds to z = -0.50 and X = 93 corresponds to z = +2.00. What are the values for the population mean and standard deviation?

ANSWER: μ = 85 and σ = 4 STEPS: First, find the distance between the two X-scores: 93-83 = 10 Next, find the corresponding z-score distance: 2- (-0.5) = 2 + 0.5 = 2.5 So you know that a z-distance of 2.5 corresponds to a raw score distance of 10. You also know that 1 z-score is equal to one standard deviation. Therefore simply take 10 and divide it by 2.5: 10/2.5 = 4. You get that one z-score or one standard deviation is equal to 4. To find the mean, use µ = x - zσ = 83 - (-0.5*4) = 83 + 2 = 85

What position in the distribution corresponds to a z-score of z = -1.00?

Below the mean by a distance equal to 1 standard deviation

A distribution with µ = 55 and σ = 6 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 = 58 from the original distribution?

X=55

A population with µ = 85 and σ = 12 is transformed into z-scores. After the transformation, what is the standard deviation for the population of z-scores?

σ = 1.00

On an exam with μ = 52, you have a score of X = 44. Which value for the standard deviation would give you the highest position in the class distribution?

σ=8