Answer:
At least 8.26 hours of daily TV watching is necessary for a person to be eligible for the interview.
Step-by-step explanation:
We are given that a newspaper article reported that people spend a mean of 6.5 hours per day watching TV, with a standard deviation of 1.7 hours.
A psychologist would like to conduct interviews with the 15% of the population who spend the most time watching TV.
<u><em>Let X = daily time people spend watching TV</em></u>
So, X ~ Normal()
The z score probability distribution for normal distribution is given by;
Z = ~ N(0,1)
where, = population mean time watching TV = 6.5 hours
= standard deviation = 1.7 hours
<u>Now, we have to find that at least how many hours of daily TV watching is necessary for a person to be eligible for the interview, that means;</u>
P(X x) = 0.15 {where x is required number of hours}
P( ) = 0.15
P(Z ) = 0.15
Since, in the z table the critical value of x which represents the top 15% probability area is given by x = 1.0364, that is;
= 1.0364
x = 6.5 + 1.762 = <u>8.26 hours per day</u>
Therefore, at least 8.26 hours of daily TV watching is necessary for a person to be eligible for the interview.