Exercise 5.3

1.

Consider the height example given above. Determine the first and third population quartiles. (Ans: 67.30204, 72.69796).

2.

In the last problem, a basketball coach remarks that the even shortest professional basketball player, exceeds the 98th percen tile in height. Does this make sense? (Help with answer: 98th percentile is 78.215).

3.

Suppose we know that scores on this exam are approximately normally distributed with mean 430 and standard deviation 50. Determine the first and third population quartiles. (Ans: 396.2755, 463.724 5).

4.

Smith College only accepts the upper 20% of people taking the exam in #3. What is the lowest score a person can make on the exam and still be acceptable to Smith College? (Ans. 472.0811).

5.

Verify that for any normal population, the probability that a measurement falls in the interval $\mu - 2\sigma$ to $\mu + 2\sigma$ is .9544997.

6.

Verify that for any normal population, the probability that a measurement falls in the interval $\mu - 3\sigma$ to $\mu + 3\sigma$ is .9973002.