# Math Help - Central limit theorem: Sample mean

1. ## Central limit theorem: Sample mean

A newspaper article reported that people spend a mean of 6 hours per day watching TV, with a standard deviation of 1.9 hours. A psychologist would like to conduct interviews with the 10% of the population who spend the most time watching TV. She assumes that the daily time people spend watching TV is normally distributed. At least how many hours of daily TV watching are necessary for a person to be eligible for the interview? Carry your intermediate computations to at least four decimal places. Round your answer to at least one decimal place.

2. Hi

You have the population mean $\mu = 6 \mbox{ and standard deviation } \sigma = 1.9$

To be eligible for the interview one needs to be in the top 10%.

This means, that 90% of the people spend less time in front of the TV than necessary for the interview.

So, $P(X\leq x) = \Phi\left(\frac{x-\mu}{\sigma}\right)=0.9$

Looking at a standard normal dist. table we see that for $P(X\leq x)$ we have $\Phi(1.28)$

Which means $\frac{x-6}{1.9}=1.28 \; \; \Rightarrow x = 8.432$

So 8.4 hours.

3. Twig, Thank you. That was one of the answers I got BUT I was so unsure because I also had a different one and w/Stats, I am ALWAYS unsure of myself.... How you all have minds that think at this level, I'll never figure that out. Once again, I appreciate your help.