A charity has found that 42% of all donors from last year will donate again this

Question

A charity has found that 42% of all donors from last year will donate again this year. A random sample of 300 donors from last year was taken. What is the standard error of the sample proportion who will donate again this year? What is the probability that more than half of these sample members will donate again this year? What is the probability that the sample proportion is between 0.40 and 0.45? Without doing the calculations, state in which of the following ranges the sample proportion is more likely to lie: 0.39 to 0.41., 0.41 to 0.43, 0.43 to 0.45, 0.45 to 0.47.

Explanation / Answer

2. p hat=0.42and n=300

a. Standard error=sqrt(p(1-p)/n)=sqrt(0.42*(1-0.42)/300)=0.028

b. P(x>0.5)=P(z>0.5-0.42/0.028)=P(z>2.86)=0.0021

c. P(0.40<x<0.45)=P(-0.71<z<1.07)=0.6188

d. It will be in group 0.41 to 0.43

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