Question

The distribution of resting pulse rates of all students at Adams High School was approximately normal with mean \mu = 80μ=80mu, equals, 80 beats per minute and standard deviation \sigma = 9σ=9sigma, equals, 9 beats per minute. Only students whose resting pulse rates are in the lower 40\%40%40, percent are eligible join the weight-lifting club. What is the maximum resting pulse rate for students who are eligible to join the weight-lifting club?

Answer 1

Answer:

Maximum beat per minute for the lower 40% can be 77.

Step-by-step explanation:

Let z* be the z-score associated to the lower 40% bound. Then

P(z<z*)=0.4 By looking one tail z-table, we can find that z*=−0.253.

Let X be the maximum pulse rate among the pulse rates in the lower 40%. Then

z*=-0.253=$\frac{X-M}{s}$ where

• X is the maximum pulse rate of the lower 40%

• M is the mean resting pulse rates of all students at Adams High School (80 beats per minute)

• s is the standard deviation of resting pulse rates of all students at Adams High School (9 beats per minute)

-0.253=$\frac{X-80}{9}$ and we get X=(-0.253×9)+80=77.723

Since beats per minute can be positivive integer, maximum beat per minute for the lower 40% can be 77