credit 1. A stemplot of ages of 18 faculity members in a represents 43 years col

Question

credit 1. A stemplot of ages of 18 faculity members in a represents 43 years college math department follows. 413 3) 24899 4 03569 5 347899 6 3 8 Find the median age of the faculty. a. b. Find the interquartile range of faculty ages. C. If the 68-year-old retires and is replaced with a 26-year-old, find the new median 46.5 2. (2 pts) Does exposure to classical music (through instrument lessons or concert attendance) improve children's scholastic performance? In a study, researchers measured the amount of exposure to classical music for many children, along with their scores on the state's academic proficiency exam. The explanatory variable in this study is: 2. Scores on ouadamic exam 3. Scores on a university exam are Normally distributed with a mean of 68 and a standard deviation of 9. Using the 68-95-99.7 rule, a. What percentage of students score above 77? b. What percent of students score lower than 50? Find the z-scores that separate the middle 80% of the distribution from the area in the tails of the standard normal distribution 4,

Explanation / Answer

3)a) According to epmerical rule 68% of the data falls within 1 standard deviation from the mean.

So 34% of data will fall above one standard deviation from the mean and 34% of data will fall below one standard deviation from the mean.

50% data will fall below the mean and 50% data will fall above the mean.

Here 77 is one standard deviation above the mean.

68 + 9 = 77

So according to emperical rule the percentage of students score above 77 = 50% - 34% = 16%

b) According to epmerical rule 95%% of the data falls within 2 standard deviation from the mean.

So 47.5% of data will fall above 2 standard deviation from the mean and 47.5% of data will fall below 2 standard deviation from the mean.

Here 50 is 2 standard deviation below the mean.

68 - 2 * 9 = 68 - 18 = 50

So according to emperical rule the percentage of students score lower than 50 = 50% - 47.5% = 2.5%

4) P(Z < z) = 0.1

   or, z = -1.28

P(Z > z) = 0.1

or, 1 - P(Z < z) = 0.1

or, P(Z < z) = 0.9

or, z = 1.28

So the required z-scores are -1.28 and 1.28.

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