Assume that the president is correct and p 30 What is the s

Assume that the president is correct and p = .30. What is the sampling distribution of  for this study?
- Select your answer -A normal distribution because np and n(1-p) are both greater than 5A normal distribution because np and n(1-p) are both less than 5A non normal distributionItem 1

What is the probability that the sample proportion will be between .20 and .40 (to 4 decimals)?

What is the probability that the sample proportion will be between .25 and .35 (to 4 decimals)?

Solution

the sampling distribution of  for this study

Normal distribution with p=0.3 and standard deviation=sqrt(p*(1-p)/n)

=sqrt(0.3*0.7/100)

=0.04582576

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A normal distribution because np and n(1-p) are both greater than 5

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So the probability that the sample proportion will be between .20 and .40 is

P(0.2<phat<0.4)

= P((0.2-0.3)/sqrt(0.3*0.7/100) <(phat-p)/sqrt(p*(1-p)/n) <(0.4-0.3)/sqrt(0.3*0.7/100))

=P(-2.18<Z<2.18)

=0.9707 (from standard normal table)

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So the probability that the sample proportion will be between .25 and .35 is

P(0.25<phat<0.35)

=P((0.25-0.3)/sqrt(0.3*0.7/100) <Z<(0.35-0.3)/sqrt(0.3*0.7/100))

=P(-1.09<Z<1.09)

=0.7243 (from standard normal table)