I have a math problem. I hardly know where to start. Can you help?

Question

Here it is.  Wow..., this is really hard to read for  me.

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 9 and standard deviation 2.5. An opinion poll asks this question of an srs of 1100 adults. We will see in chapter 9 that in this situation the sample mean response x has approximately the normal distribution with mean 9 and standard deviation 0.075. What is P(8<=x-var<=10), the probability that the statistic x-var estimates the parameter mean to within +/- 1?

 

Answer 1

'The question is asking you to find the average number of close friends a person has. Do to so, they did a srs (simple random sample) with an N=1000 adults. You also learned in Chapter 9 that this type of sampling will have a normal distribution of the response(or the x-var). And you're told that the sample mean of x-var=9, and the sample standard deviation =0.075. So to calculate the probability that the statistic x-var, estimates the parameter mean to within +/- 1. In other words, you being asked to calculate the probability that the (8<=x-var<=10). the 8 & 10 are simply 9-1=8 and 9+1=10. Now you just need to convert 'x-var' to a standard normal variable (this makes it easier to solve & you can use tables to look up the actual probabilities. They're usually tables in the back of your book with the table of the normal distributions. You'll need to convert 8 & 10 to their standard normal equivalents & then look up those numbers in your table. I think Robert did that work for you. I hope that's a sufficient explanation, not sure what else I could have added. Good Luck, MMarla

Answer 2

P(8<=x-var<=10) ~ 1, since |(x-μ)|/σ > 13.

Attn: P(|(x-μ)|/σ = 3) = 99.7