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# Normal Probability Calculation of Grades

1. A z-score of z = +3.00 indicates a location that is ____.
A) near the center of the distribution
B) slightly above the mean
C) far above the mean in the extreme right-hand tail of the distribution
D) The location depends on the mean and standard deviation for the distribution.
2. For a distribution of scores, which of the following z-score values represents the most extreme location on the left-hand side of the distribution?
A) z = +1.00
B) z = +2.00
C) z = -1.00
D) z = -2.00
3. For a distribution of scores, which of the following z-score values represents the location closest to the mean?
A) z = +0.50
B) z = +1.00
C) z = -1.00
D) z = -2.00
4. Last week Sarah had exams in Math and in Spanish. On the math exam, the mean was m = 40 with s = 5, and Sarah had a score of X = 45. On the Spanish exam, the mean was m = 60 with s = 8 and Sarah had a score of X = 68. 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.
5. A random sample requires that ____.
A) every individual has an equal chance of being selected
B) the probabilities cannot change during a series of selections
C) there must be sampling with replacement
D) All of the other choices are correct.
6. Probability values are always ____.
A) greater than or equal to 0
B) less than or equal to 1
C) positive numbers
D) All of the other choices are correct.
7. If random samples, each with n = 4 scores, are selected from a normal population with m = 80 and s = 10, then the distribution of sample means will have a standard error of ____.
A) 2.5 points
B) 5 points
C) 10 points
D) 80 points
8. The standard deviation of the distribution of sample means is called ____.
A) the expected value of M
B) the standard error of M
C) the sample mean
D) the central limit mean
9. A random sample of n = 4 scores is obtained from a normal population with m = 40 and s = 6. What is the probability of obtaining a mean greater than M = 46 for this sample?
A) 0.3085
B) 0.1587
C) 0.0668
D) 0.0228
10. A random sample of n = 4 scores is obtained from a normal population with m = 20 and s = 4. What is the probability of obtaining a mean greater than M = 22 for this sample?
A) 0.50
B) 1.00
C) 0.1587
D) 0.3085

#### Solution Summary

The solution provides step by step method for the calculation of normal probability. Formula for the calculation and Interpretations of the results are also included.

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