I need help the followng Statistics questions involcing probability. (Please exp

Question

I need help the followng Statistics questions involcing probability. (Please explain all answers in clear and concise manner and round to four decimal places)

ABC Manufacturing has a policy that it will reject a shipment of parts from its supplier if inspectors find any defective parts in a random sample of 4 parts from the shipment. The supplier has been in business many years and has a long-term defective rate for parts of 7.1%. Question 1 What is the probability that a shipment will be rejected after a given sample of parts is checked? A local university ound it could classify its students into one of three general categories: morning st ents 45% the morning students, 22% of the afternoon students, and 17% of the evening students live on campus. a ter ons aer s 5% and evening students Question 2 What is the probability a non-Afternoon student does not live on campus? Of 50 bank accounts at a small bank, 26 accounts have values of less than $1,000 and the rest have values of at least $1,000. Suppose 6 accounts are randomly sampled. (See exercise 9 on page 189 of your textbook for a similar problem.) Question 3 What is the probability that exactly 5 of the 6 accounts have values of at least $1,000?

Explanation / Answer

1) P(defective) = 0.071

n = 4

P(at least 1 defective) = 1 - P(no defective)

= 1 - (1-0.071)4

= 0.2552

2) percentage of evening students = 100 - 45 - 35 = 20%

P(non afternoon student does not live on campus) = P(morning student does not live on campus) + P(eveningn student does not live on campus)

= 0.45 * (1 - 0.36) + 0.2 * (1 - 0.17)

= 0.454

3) P(at least 1000) = (50 - 26) / 50 = 0.48

n = 6

P(X = x) = 6Cx * 0.48x * (1 - 0.48)6-x

P(X = 5) = 6C5 * 0.485 * 0.521 = 0.0795

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