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The ages of members of a cycling club are normally distributed with a mean of 35 years ar standard deviation of 5 years. What percentage of the members of the club are aged between 25 and 40?

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Final answer:

Using the normal distribution properties and z-scores for 25 and 40, we find that approximately 81.85% of the cycling club members are aged between 25 and 40.

Step-by-step explanation:

To find the percentage of cycling club members aged between 25 and 40, we will use the properties of the normal distribution. The mean age is given as 35 years with a standard deviation of 5 years. This problem requires us to calculate the z-scores for the ages 25 and 40 and then use the standard normal distribution to find the corresponding percentages.

The z-score for age 25 is calculated as follows:
Z = (X - μ) / σ
Where Z is the z-score, X is the value (age), μ is the mean, and σ is the standard deviation.
For age 25: Z = (25 - 35) / 5 = -2

For age 40: Z = (40 - 35) / 5 = 1

Using standard normal distribution tables or a calculator, we find the area under the curve to the left of the z-score for age 25 (z=-2) and for age 40 (z=1). The area between these two z-scores gives us the percentage of members aged between 25 and 40.

For z=-2, the area to the left is approximately 2.28%, and for z=1, it is approximately 84.13%. To find the percentage between these ages, we subtract the area for z=-2 from the area for z=1, which yields approximately 81.85%.

Therefore, approximately 81.85% of the members are aged between 25 and 40.

User David Bukera
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