Mathematics, 15.11.2019 19:31 ddea4081

In a study of exercise, a large group of male runners walk on a treadmill for six 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 rates for male nonrunners after the same exercise have the n(130, 17) distribution.
(a) what percent of the runners have heart rates above 130?
(b) what percent of the nonrunners have heart rates above 130?

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Answers

Using the normal probability relation, the probabilities that a runner and non - runner has a heart rate above 130 are 0.01876 and 0.5 respectively

Using the Zscore relation :

Zscore = (x - μ) ÷ σ

1.)

Runner with heart rate above 130 :

Mean, μ = 104Standard deviation, σ = 12.5

For X > 130 :

Zscore = (130 - 104) ÷ 12.5 = 2.08

P(Z > 2.08) = 1 - P(Z < 2.08)

Using a normal distribution table :

P(Z > 2.08) = 1 - 0.98124 = 0.01876

2.)

Non - Runner with heart rate above 130 :

Mean, μ = 130Standard deviation, σ = 17

For X > 130 :

Zscore = (130 - 130) ÷ 17 = 0

P(Z > 0) = 1 - P(Z < 0)

Using a normal distribution table :

P(Z > 0) = 1 - 0.5 = 0.5

Therefore, probability that a non - runner has a rate rate above 130 is 0.5

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Answer from: williamnason123

a) 1.88% percent of the runners have heart rates above 130.

b) 50% percent of the nomrunners have heart rates above 130.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

(a) What percent of the runners have heart rates above 130?

In a study of exercise, a large group of male runners walk on a treadmill for six minutes. Their heart rates in beats per minute at the end vary from runner to runner according to the N(104,12.5) distribution. This means that $\mu = 104, \sigma = 12.5$ .