1. A distribution of values is normal with a mean of 140 and a standard deviatio

Question

1. A distribution of values is normal with a mean of 140 and a standard deviation of 2.

Find the interval containing the middle-most 30% of scores:

Enter your answer using interval notation. Example: [2.1,5.6)

Please tell me how to solve using excel.

2. A teacher informs her organic chemistry class (of 500+ students) that a test was very difficult, but the grades would be curved. Scores on the test were normally distributed with a mean of 28 and a standard deviation of 9.1. The maximum possible score on the test was 100 points. Because of partial credit, scores were recorded with 1 decimal point accuracy. (Thus, a student could earn a 28.1, but not a 27.21.)
Please tell me how to solve in excel as well.
The grades are curved according to the following scheme. Find the numerical limits for each letter grade.

Please tell me how to solve in excel as well.

Letter Scheme Interval A Top 10% B Scores above the bottom 65%
and below the top 10% C Scores above the bottom 35%
and below the top 35% D Scores above the bottom 10%
and below the top 65% F Bottom 10%

Explanation / Answer

3. We have mean = 0, stdev = 1

So, P(Z>c) = .3249

So, 1-P(Z>c) = P(Z<=c) = 1-.3249 = .6751

So, lookinng at Z table we have z value of .455 for a cumulative area of .6751

So, c-0 /1 - .455

c = .455 oC

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