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# Probability Assistance

1. A minor league baseball manager boasted about his players' batting averages. Below is a frequency distribution of those averages.
Batting Averages Frequency Cumulative Frequency
270.5 to 279.5 2 2
279.5 to 288.5 3 5
288.5 to 297.5 3 8
297.5 to 306.5 5 13
306.5 to 315.5 9 22
315.5 to 324.5 4 26
324.5 to 333.5 3 29
333.5 to 342.5 1 30

Find the grouped median batting average.

299.3
307.1
308.5
311.0

2. Mary Mischief came home from school one day and told her mother that she scored an 80 on her standardized reading test and an 84 on her standardized math test. Mary's mother was ecstatic about her daughter's academic achievements. However, at the PTA meeting the following week, Mary's teacher explained that the reading test had a mean of 90 and a standard deviation of 5 while the math test had a mean of 100 and a standard deviation of 8. Should Mary's parents still be jubilant? Explain.
Yes, Mary's scores are high enough to show genuine achievement when viewed from the lens of 100.
No, Mary's scores are one standard deviation below the mean on both tests.
No, Mary's scores are two standard deviations below the mean on both tests.
Mixed reaction because Mary's scores are low in reading, but are somewhat higher in math.

3. Grades on a tenth-grade geometry final examination for Martha Crenshaw's private school class were: 78, 80, 81, 82, 85, 86, 86, 88, 90, 90, 91, 92, 94, 95, 96, 97, 99, 100, 100, 100, 100. (You can thank Mrs. Crenshaw for arranging them in order for you.) What grade represents the 75th percentile?

95
96
97
99

4. An information technology professor wants to make a box plot of grades on a quiz, whose scores ranged from 0 to 50. Below is his grade distribution.
25, 36, 20, 40, 50, 35, 34, 48, 42, 50
What values represent the lower hinge and upper hinge, respectively?

36 and 40
36 and 42
35 and 42
34 and 48

5. Inspect the following data set that represents the prices of homes given in thousands of dollars, rounded.
150, 166, 145, 178, 142, 140, 300, 125, 195, 205, 200, 285, 168, 255
If a box plot were to be drawn from this raw data, where would the longer whisker representing an outlier be located?
This longer line segment should be drawn to the left of the median.
This longer line segment should be drawn to the right of the median.
There are no outliers; so, the length of whiskers is irrelevant.
There is no way to tell, given only the raw data set.

#### Solution Preview

1. Median = (30/2-13)*(315.5-306.5)/9 + 306.5
= 308.5

2. No, Mary's scores are two standard deviations below the mean on both tests.
...

#### Solution Summary

This Solution contains calculations to aid you in understanding the Solution to this question.

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