# Homework Help: Finding the probability that tge sample proportion is within 0.05 of the population

1. Oct 22, 2014

### werson9339

1. The problem statement, all variables and given/known data
Person A claims that the porportion of household installed with solar heater is 0.15. A random sample of 250 household iataken.
Assuming the claim of person A is true, finding the probability that tge sample proportion is within 0.05 of the population proportion.

2. Relevant equations

3. The attempt at a solution
the ans given is P (|pˆ-p| ) < 0.05 ,

i do it in this way .... my reason is to find the z value using confidence interval method , since confience interval is defined as how many percent are you sure that the sample mean lies in the population mean interval

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2. Oct 22, 2014

### werson9339

3. Oct 22, 2014

### RUber

I think you may have forgotten to take off the other tail.
p(z<2.214) is the probability that the sample proportion will be less than .15+.05.
p(z<-2.214) is the probability that the sample proportion will be less than .15-.05.

4. Oct 22, 2014

### Ray Vickson

I do not look at work done in posted files. If you type out your work I would be willing to look at it. I think the majority of helpers here have a similar policy.