Chapter 7, Review Exercises, Question E51 About 68% of the people in China live

Question

Chapter 7, Review Exercises, Question E51 About 68% of the people in China live in rural areas. Suppose a random sample of 180 Chinese people is taken. a. Describe the shape, mean, and standard error of the sampling distribution of P, the proportion of people in the sample who live in rural areas. Shape Mean Standard error (round to four decimal places) b, what is the probability that 75% or more in the sample live in rural areas? (round to four decimal places) c. What values of P would be rare events? Round to three decimal places. Values less than or larger than d. What is the probability that 130 or more in the sample live in rural areas? (round to four decimal places)

Explanation / Answer

a)
Shape - Normal curve

Mean = 0.68

SE = sqrt(0.68*0.32/180) = 0.0348

b)
P(X > 0.75)
= P(z > (0.75 - 0.68)/0.0348)
= P(z > 2.0115)
= 0.0221

c)
We will consider an event rare if it occurs with probabitity less than 0.025
z-value for this is 1.96

pcap = 0.68 - 1.96*0.0348 = 0.6118
pcap = 0.68 + 1.96*0.0348 = 0.7482

Values less than 0.6118 or larger than 0.7482

d)
pcap = 130/168 = 0.7738
P(X > 0.7738)
= P(z > (0.7738 - 0.68)/0.0348)
= P(z > 2.6954)
= 0.0035

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

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