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