The question reads:
"How many close friends do you have? Suppose that the number of close friends adults claim to have varies from person to person with mean and standard deviation . An opinion poll asks this question of an SRS of 1100 adults. We will see in the next chapter that in this situation the sample mean response has approximately the Normal distribution with mean 9 and standard deviation 0.075. What is , the probability that the statistic estimates the parameter to within ?"
I started by saying that we have N(9, 2.5) and so:
P(8< x < 10) = ((8-9)/2.5 < Z < (10-9)/2.5)
= P(-.4 < Z < .4)
= 0.6554 - 0.3446
= 0.3108
Unfortunately, the answer is incorrect. I considered, too, the statement that "in this situation, sample mean response has approximately N(9, 0.075), but I wind up with P(-13.333 < Z < 13.333) which is way off. At what point did I go wrong? My apologies for having to cut and paste, and for the notation being a little off, I'm still learning the ropes with inputting math equations on forums.