Question

1. Adapted from Exercise 3.32 in the textbook. A large group of male runners walk on treadmill for 6 minutes. Their heart rates in beats per minute at the end vary from runner to runner according to the N(104, 12.5) distribution. The heart rate for male non-runners after the same exercise have the N(130, 17) distribution.

(a) What percent of runners have heart rates above 135? What percent of non-runners have heart rates above 135?

(b) What is the median heart rate for runners? What is the IQR?

(c) What percent of runners have heart rates between 110 and 125?

(d) A non-runner has a heart rate of 120. What is the standardized score for this runner? What does the z-score tell us?

(e) Lower heart rates are often associated with healthier, more efficient hearts. Below what heart rate would a non-r

Answer 1

According to the question, a large group of male runners walk on treadmill for 6 minutes. Their heart rates in beats per minute at the end vary from runner to runner according to the N(104, 12.5) distribution. The heart rate for male non-runners after the same exercise have the N(130, 17) distribution.

Define, X: heart rate for male runners after the exercise;

Y: heart rate for male non-runners after the exercise

Then,

(a)

Percent of runners have heart rates above 135

%

%

%

%

%

%

%

Percent of non-runners have heart rates above 135

%

%

%

%

%

%

%

(b)

Median heart rate for runners

=mean of heart rate foir runners [As heart rate for runners follow a normal distribution]

For runners, First quartile of heart rates(Q1)

For runners, Third quartile of heart rates(Q3)

So,

(c)

Percent of runners have heart rates between 110 and 125

%

%

%

%

%

(d)

A non-runner has a heart rate of 120.

Standardized score for this non-runner

The non-runner lies is in the lower half of the distribution the heart rates follow. In fact, the non-runner's heart rate just below the median. So, we can conclude that his heart-rate is almost average.

(e) THIS QUESTION IS INCOMPLETE.