Mathematics, 31.07.2021 19:00 mathmeup

In a health club, research shows that on average, patrons spend an average of 46.2 minutes on the treadmill, with a standard deviation of 4.8 minutes. It is assumed that this is a normally
distributed variable. Find the probability that randomly selected individual would spent
between 30 and 40 minutes on the treadmill.

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As the problem states, the variable has a normal distribution, and thus, concepts of this distribution are used to solve this question.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

In a health club, research shows that on average, patrons spend an average of 46.2 minutes on the treadmill, with a standard deviation of 4.8 minutes.

This means that $\mu = 46.2, \sigma = 4.8$

Find the probability that randomly selected individual would spent between 30 and 40 minutes on the treadmill.

This is the p-value of Z when X = 40 subtracted by the p-value of Z when X = 30.

X = 40

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

$Z = \frac{40 - 46.2}{4.8}$

Z = -1.29

Z = -1.29 has a p-value of 0.0985

X = 30

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

$Z = \frac{30 - 46.2}{4.8}$

Z = -3.38

Z = -3.38 has a p-value of 0.0004.

0.0985 - 0.0004 = 0.0981

Thus, 0.0981 = 9.81% probability that randomly selected individual would spent between 30 and 40 minutes on the treadmill.

For another example of the normal distribution, you can check

Answer from: Quest

i believe the correct answer is option 4.principalities were small territories that were run by russian rulers.

which statement correctly defines principalities in northern asia in the 1200s? principalities were small territories that were run by russian rulers.

hope i could ! : )

Answer from: Quest

dalila is incorrect. the whisker on the left is very long, going all the way out to 5. the whisker goes from 5 to 30, so it has a spread of 25. the rest of the box plot values are closer together, so 5 is an outlier

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