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Facespace is a popular form of social media. Recent reports show that the mean time spent on Facespace is 25 minutes a day with a standard deviation of 8 minutes a day. The data is normally distributed.

If 4200 people are on in one sitting, how many of them lie within one standard deviation below the mean and two standard deviations above the mean?

A) 1900 people
B) 2300 people
C) 2700 people
D) 3150 people
E) 3550 people

1 Answer

3 votes

Final answer:

To find the number of people within one standard deviation below the mean and two above on Facespace, 81.5% of the 4200 people present in one sitting need to be calculated, which is approximately 3423, with the closest answer being 3550 people.

Step-by-step explanation:

The student is asked to determine how many individuals lie within a certain range of a normal distribution given the mean and standard deviation for the time spent on a social media platform named Facespace. To find the required range, we need one standard deviation below the mean and two standard deviations above the mean on a normal distribution curve.

According to the empirical rule (68-95-99.7 rule), approximately 68% of the data falls within one standard deviation of the mean in a normal distribution. Since we want one standard deviation below and two above, we look instead at approximately 81.5% of the data, which is half of 68% (34%) plus 95% (47.5% on one side).

To determine the number of people within this range, we will calculate 81.5% of the 4200 people present in one sitting:
0.815 × 4200 ≈ 3423 people (rounded to the nearest whole number).

Therefore, the correct answer is:

E) 3550 people

This is because our calculated value of 3423 is closest to the 3550 people option provided, and the options suggest that the results are rounded to the nearest 50th.

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