High School

We appreciate your visit to Problem 1 In a study of exercise a large group of male runners walk on a treadmill for 6 minutes Their heart rates in beats. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

Problem 1: In a study of exercise, a large group of male runners walk on a treadmill for 6 minutes. Their heart rates in beats per minutes at the end vary from runner to runner according to a normal distribution with mean µ = 104 and standard deviation σ = 12. Let X be the heart rate in beats per minutes of a randomly chosen runner, that is, X ∼ N (104,12). Use Microsoft Excel to compute the following probabilities: The probability that a randomly selected male runner has heart rate between 89 and 119 at the end of the 6 minutes’ walk? That is, what’s P (89 < X < 119). The probability that a randomly chosen male runner has heart rate of 134 or higher at the end of 6 minutes’ walk, P (X ≥ 134). The probability that a randomly chosen male runner has heart rate lower than 89 at the end of 6 minutes’ walk, P (X ≤ 89).

Answer :

Final answer:

In Excel, the NORM.DIST function is used to calculate probabilities for a normal distribution. These probabilities can be computed by converting the raw heart rates to z-scores, and then using the z-scores in NORM.DIST to find the desired probabilities.

Explanation:

The subject of the question is statistics, specifically it is dealing with the computation of probabilities for a normal distribution. The software suggested for these computations is Microsoft Excel. Excel has built-in functions to handle these kinds of computations.

First, let's convert the raw scores (heart rates) into z-scores. The z-score for a value x is calculated as (x - µ) / σ. For instance, for 89 bpm, the z-score would be (89 - 104) / 12 = -1.25. Similarly, calculate the z-scores for 119 and 134.

  1. To find P(89 < X < 119), use the Excel function =NORM.DIST(119, 104, 12, TRUE) - NORM.DIST(89, 104, 12, TRUE). This computes the cumulative probabilities for 119 and 89 and subtracts the latter from the former.
  2. To find P(X ≥ 134), calculate 1 - NORM.DIST(134, 104, 12, TRUE), because the function NORM.DIST gives the cumulative probability up to the given value, and we want the probability from that value upwards.
  3. P(X ≤ 89) can be calculated directly with the function NORM.DIST(89, 104, 12, TRUE).

Learn more about Excel Normal Distribution here:

https://brainly.com/question/33807468

#SPJ11

Thanks for taking the time to read Problem 1 In a study of exercise a large group of male runners walk on a treadmill for 6 minutes Their heart rates in beats. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada