Over a typical quarter of the year, about 75 million people, or one-third of the

Question

Over a typical quarter of the year, about 75 million people, or one-third of the total Internet population, buy goods on line to be shipped to them. Of those75 million people, approximately 67% select Economy Ground shipping, which takes 5-7 days. A survey of 1000 randomly selected online shoppers is to be taken. a) Verify the three conditions for the central limit theorem to apply in this situation. b) What is the probability that the proportion of shoppers in the sample who select Economy Ground shipping for their order is larger than 70%?

Explanation / Answer

Solution:-

a) 1) Randomization Condition: The data must be sampled randomly. In thsi survey it is given that 1000 online shoppers are randomly selected.

2) Independence Assumption: The sample values must be independent of each other. This means that the occurrence of one event has no influence on the next event. In this survey we have taken a random sample so we can assume this to be independent.

3) Sample Size Assumption: The sample size must be sufficiently large. In general a sample size of 30 is considered sufficient if the sample. In thsi survey sample size is 1,000.

b) The probability that the proportion of shoppers in the sample who select economy ground for their order is larger than 70% is P(x > 700) = 0.0195.

p = 67/100 = 0.67

n = 1,000

x = 0.70 × 1000

x = 700

By applying binomial distribution:-

P(x, n, p) = nCx *px *(1 - p)(n - p)

P(x > 700) = 0.0195

Related Questions

Navigate

• Browse (All)
• Browse O
• Subjects

---

---

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