Quiz 10.3

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

Because the score (44) is lower than the mean (52), you would want a standard deviation that is as large as possible to get a better position.

On an exam with μ = 52, you have a score of X = 56. Which of the following values for the standard deviation would give you the highest position in the class distribution?​

Because your score (56) is higher than the mean (52), you would want to get away from the rest of the class as far as possible so that you can be distinguished high performing outlier. In this case, you would want to have a standard deviation that is as small as possible

Which of the following represents the deviation score?​

Deviation is just the difference between a score and the mean. It is the numerator part of the z-formula.

Last week Sarah had exams in Math, Spanish and English. 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 s = 8 and Sarah had a score of X = 68. On the English exam, the mean was µ = 70 with s = 8 and Sarah had a score of X = 78. For which class should Sara expect the better grade?​

If you just apply the z-formula and eyeball the scores, you will see that the z-score for all exams is equal to 1. Therefore, Sarah did equally well in all exams.

Which of the following z-score values represents the location closest to the mean?​

The mean is represented by a z-score of zero. Therefore, the close a z-score is to zero, the closer it is to the mean.

For a population with a standard deviation of σ = 6, what is the z-score corresponding to a score that is 12 points above the mean?​

The problems says that a score is 12 points above the mean, which is the deviation score. If the z-formula is: z= (x-μ)/ σ , the numerator is 12, and we know that σ=6. Therefore, z-score is 12/6 = 2

What position in the distribution corresponds to a z-score of z = +2.00?​

The z-score specifies the position of a score above or below the mean in the distribution

Last week, Sarah had exams in Math, Spanish, and English. On the Math exam, the mean was µ = 30 with s = 5, and Sarah had a score of X = 45. On the Spanish exam, the mean was µ = 60 with s = 8 and Sarah had a score of X = 68. On the English exam, the mean was µ = 70 with s = 8 and Sarah had a score of X = 70. For which class should Sara expect the better grade?​

To answer this question you would need to find the z score for each exam. Math: (45-30)/5= 3 Spanish: (68-60)/8 = 1 English: (70-70)/8 = 0 You can see that the highest z-score is 3, which means that Sarah did the best in her Math exam relative to her classmates who took the exam. Her score was just slightly higher than average for Spanish, and she was just average for English.

For a p opulation with µ = 80 and σ = 10, what is the z-score corresponding to X = 95?​

Z= (95-80)/10 = 1.5