A researcher is interested in the age at which adolescents get their first payin

Question

A researcher is interested in the age at which adolescents get their first paying job. She surveyed a simple random sample of 150 adolescents who have had at least one paying job before the age of 19. The distribution of the ages was found to be approximately normal with a mean of 15.2 years and a standard deviation of 1.6 years. According to the empirical rule, between which two ages do approximately 95% of the adolescents get their first paying job? a. 13.2 years and 17.2 years b. 15.2 years and 18.4 years c. 12 years and 15.2 years d. 12 years and 18.4 years e. 13.6 years and 16.8 years

Explanation / Answer

As per empirical rule of 68- 95 -99.7 of empirical rule, it is evident that 95% values fall within two standard deviations.

So, as per given question mean = 15.2 years

standard deviation = 1.6 years

so 95% value will fall under +- 2 standard deviation

Mean +- 2 * standard deviation = 15.2 +- 2 * 1.6 = ( 12, 18.4)

so answer is d 12 years and 18.4 years.

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