# statistics

2. Why is it important to know the mean and standard deviation for a data set when applying the empirical rule?

3. If we are focused on 68% of the normal distribution, what percentage of the distribution is left in the upper tail only?

4. What value separates the 50% of the distribution from the other 50% of the distribution?

Consider this scenario for questions 5 - 8.

A standardized test was given to a set of high school juniors and the distribution of the data is bell shaped. The mean score is 800 and the standard deviation is 120.

5. Between which two scores did 95% of the students score?

6. To qualify for a special summer camp for accelerated students, a student must score within the top 16% of all scores on the test. What score must a student make to qualify for summer camp?

7. What score is 1/2 standard deviation above the mean?

8. A student scores 900 on the test. How many more points did the student need to qualify for summer camp?

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1. 2. What empirical rule? Look at the problems you are given afterward.

3. (1-.68)/2 = ? (This is assuming that the 68% are about the mean of a normal distribution.)

4. Look at the definitions of they three measures of central tendency.

5. Z = (score-mean)/SD

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability (±.475) related to the Z scores. Insert in above equation and solve.

6. Use same table and equation.

7. Z = .5 Use equation.

8. Relate to answer on 6.

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2. A student has a mean score of five tests taken. What score must she obtain on her next test to have a mean average of 88 on all six tests?

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