The sampling distribution of p is approximately Normal when the sample size n is

Question

The sampling distribution of p is approximately Normal when the sample size n is "larger." What conditions need to be met in order to use the Normal approximation to the sampling distribution ofnp > 10 (u -p) > 10 According to government data. 22% of American children under the age of 6 live in households with incomes less than the official poverty level. A study of learning in early childhood chooses an SRS of 300 children. 5. What is the probability that more than 20% of the sample are from poverty households? (Remember to check that you can use the Normal approximation.)

Explanation / Answer

n=300

p=0.22

np=300*0.22 =66 which is > 10

n(1-p)=300*0.78 =234 which is > 10

we can use normal approximation.

Standard deviation = sqrt(p*(1-p)/n)

= sqrt(0.22*0.78/300) =0.0239

Z value for 0.20, z=(0.20-0.22) /0.0239 =-0.84

P( p >0.20) = P( z > -0.84)

=0.7995

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.