Probability of Sample Proportion Within 0.05 of Population

[werson9339]

Homework Statement

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.

Homework Equations

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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[werson9339]

anyone can answer please? thanks in advance!

 

[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.

 

[Ray Vickson]

anyone can answer please? thanks in advance!

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.