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Use the 68-95-99.7 rule to find the proportion of runners whose body weight is between 48.7 kg and 67.9 kg.

Answer :

Based on the complete question, the Normal Distribution Graph will resemble the one in the figure attached.

Also, note that using the 68-95-99.7 rule, the proportion of runners between 48.7 and 67.9 kg is 0.8385.

What is the 68-95-99.7 rule?

The 68-95-99.7 rule, also known as the empirical rule, is a statistician's shorthand for remembering the percentage of values in a normal distribution that fits within an interval estimate: 68%, 95%, and 99.7% of the variables lie within one, two, and three standard deviations of the mean, correspondingly.

To compute the proportion of runners whose body weight is between 48.7 and 67.9 kg with the help of the 68-95-99.7 rule:

We know given that:

The mean = 63.1 and

the standard deviation (SD) = 4.8.

Where the weight is 67.9kg, we know that the distance between this and the mean is 4.8, that is;

67.9 - mean

= 67.9 - 63.1

= 4.8 [1*SD]

In the same way,
48.7 corresponds to 48.7-63.1 = -14.4 [ -3*SD]

Hence, based on the rule,

  • the probability of the weight occurring between -1*SD and 1*SD = 68%; and
  • the probability of the weight occurring between -3*SD and 3*SD = 99.7%.
  • Therefore, the probability of the weight occurring between -3*SD and 1*SD = (99.7+68)/2

= 83.85%

= 0.8385.

Learn more about Normal Distribution:

https://brainly.com/question/4079902

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Full Question:

A study of elite distance runners found a mean body weight of 63.1 Kilograms (kg), with a standard deviation of 4.8kg.

  • Assuming the distribution of weights is approximately normal, make a sketch of the weight distribution (like the one below) with a horizontal axis marked in kilograms.
  • Use the 68-95-99.7 rule to find the proportion of runners whose body weight is between 48.7 and 67.9 kg

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