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There are approximately one billion smartphone users in the world today. In the United States, the ages of smartphone users between 13 and 55 approximately follow a normal distribution with an approximate mean of 37 years and a standard deviation of 8 years. Using the 68-95-99.7 rule, what percent of smartphone users are between 29 and 53 years old?

(Enter your answer as a percent to one decimal place. Do not include the % symbol.)

a) 84.1
b) 68.0
c) 95.4
d) 99.7

Answer :

Final answer:

95.4 percent of smartphone users are between 29 and 53 years old.

Therefore, the correct option is c) 95.4.

Explanation:

To find the percentage of smartphone users between 29 and 53 years old, we use the 68-95-99.7 rule, which states that approximately 68% of the data falls within one standard deviation from the mean, 95% within two standard deviations, and 99.7% within three standard deviations of the mean for a normal distribution.

Given that the mean age is 37 years and the standard deviation is 8 years, we calculate the lower boundary for the age group (29) by finding how many standard deviations below the mean it is: (29 - 37) / 8 = -1. Similarly, for the upper boundary (53), it's (53 - 37) / 8 = 2.

Since approximately 68% of the data falls within one standard deviation from the mean, and 95% within two standard deviations, the percentage of smartphone users between 29 and 53 years old falls within two standard deviations. Thus, we find the percentage between -1 and 2 standard deviations from the mean in the normal distribution table, which is 95.4%.

Therefore, the percent of smartphone users between 29 and 53 years old is approximately 95.4%. Therefore, the correct option is c) 95.4.

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