please help me answer this

Question

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 15% 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.

Answer 1

To find out who is eligible for the interview, you can use the concept of z-scores in a normal distribution. A z-score tells you how many standard deviations an element is from the mean. The psychologist is interested in the top 15% of the population, which corresponds to the 85th percentile (100% - 15% = 85%).

Given Data:

1. Mean = 6 hours
2. Standard Deviation = 1.9 hours

Z-Score for 85th Percentile:

1. The z-score for the 85th percentile is approximately 1.0364.

Calculate the Threshold:

1. To find the actual score, use the formula: X = Mean + (Z-score * Standard Deviation)
2. In this case, X = 6 + (1.0364 * 1.9)

After calculating, the threshold for daily TV watching time to be eligible for the interview is 8.0 hours. This corresponds to the top 15% of the population.

Thank you,

Ben

Answer 2

Hi Renard,

This involves the classic equation in elementary statistics:

z=(x-mu)/sigma

z=z-score, explained below

x=value you are looking for

mu=mean

sigma=standard deviation

Now, we were not given a z-score, but we were given a probability, the top 15%. This equates to the 85th percentile and above, so we search the interior of the z-table for 0.85, its decimal equivalent. The closest I can find is 0.8508 at z=1.04.

So, for our problem:

z=1.04

x=x, number of TV hours we are looking for

mu=6

sigma=1.9

Substituting:

1.04=(x-6)/1.9

Multiply both sides by 1.9

1.976=x-6

Add 6 to both sides:

x=7.976

Someone would have to watch at least 7.976 hours--basically 8 hours--of TV to be eligible for the interview. I hope this helps.