Question

Statistics For Business And Economics

Acceptance sampling is a method that uses small random samples from incoming shipments of products to assess the quality of the entire shipment. Typically, a random sample of size n is selected from a shipment, and each sampled item is tested to see whether it meets quality specifications. The number of sampled items that do not meet specifications is denoted by x. Aslong as x does not exceed a pre specified integer c, called the acceptance number, then the entire shipment is accepted for use. If x exceeds c, then the shipment is returned to the vendor.In practice, because n is usually small in comparison to the number of items in a shipment, a binomial distribution is used to describe the random variable x.

a. Suppose a company uses samples of size n = 10 and an acceptance number of c = 1 to evaluate shipments. If 10% of the items in a certain shipment are defective, what is the probability that this shipment will be returned to the vendor?

b. Suppose that a certain shipment contains no defective items. What is the probability that the shipment will be accepted by the sampling plan in part (a)?

c. Rework part (a) for shipments that are 5%, 20%, and 50% defective.

d. Let t denote the proportion of defective items in a given shipment. Use your answers toparts (a)-(c) to plot the probability of accepting a shipment (on the vertical axis) against Tt=0, .05, .10, .20, and .50 (on the horizontal axis). Connect the points on the graph with a smoothcurve. The resulting curve is called the operating characteristic (OC) curve of the sampling plan.It gives a visual summary of how the plan performs for shipments of differing quality.

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Question 45696

Statistics For Business And Economics

(1 point) A biotechnology company produced 182 doses of somatropin, including 12 which were defective. Quality control test 14 samples at random, and rejects the batch if any of the random samples are found defective. What is the probability that the batch gets rejected?

Question 45695

Statistics For Business And Economics

(1 point) Assume that the monthly worldwide average number of airplaine crashes of commercial airlines is 2.2. What is the probability that there will be
(a) at most 5 such accidents in the next month?
(b) less than 4 such accidents in the next 3 months?
(c) exactly 8 such accidents in the next 5 months?

Question 45694

Statistics For Business And Economics

(1 point) A certain typing agency employs two typists. The average number of errors per article is 1 when typed by the first typist and 3.2 when typed by the second. If your article is equally likely to be typed by either typist, find the probability that it will have no errors.

Question 45693

Statistics For Business And Economics

(1 point) The mean number of patients admitted per day to the emergency room of a small hospital is 2. If, on any given day, there are only 7 beds available for new patients,what is the probability that the hospital will not have enough beds to accommodate its newly admitted patients?

Question 45692

Statistics For Business And Economics

nt) Given that x is a random variable having a Poisson distribution, compute the following:
\text { (a) } P(x=7) \text { when } \mu=0.5
P(x \leq 6) \text { when } \mu=4.5
\text { c) } P(x>3) \text { when } \mu=5.5
P(x<9) \text { when } \mu=4.5

Question 45691

Statistics For Business And Economics

B. Compute the probability that in the next 8 hours, more than 24 cars will arrive.
A. Determine the probability that over the next hour, only one car will arrive.
Cars arriving for gasoline at a Shell station follow a Poisson distribution with a mean of 9 per hour.

Question 45690

Statistics For Business And Economics

Complaints about an Internet brokerage firm occur at a rate of 5 per day. The number of complaints appears to be Poisson distributed.
A. Find the probability that the firm receives 4 or more complaints in a day.
Probability =%3D
B. Find the probability that the firm receives 22 or more complaints in a 5-day period.
Probability =

Question 45689

Statistics For Business And Economics

Flaws in a carpet tend to occur randomly and independently at a rate of one every 150 square feet. What is the probability that a carpet that is 9 feet by 13 feet contains noflaws?
Probability:

Question 45688

Statistics For Business And Economics

The number of accidents that occur at a busy intersection is Poisson distributed with a mean of 3.4 per week. Find the probability of the following events.
.4 or more accidents occur in a week.
A. No accidents occur in one week.
One accident occurs today.

Question 45687

Statistics For Business And Economics

(1 point) An airline company is considering a new policy of booking as many as 271 persons on an airplane that can seat only 260. (Past studies have revealed that only 89%of the booked passengers actually arrive for the flight.) Estimate the probability that if the company books 271 persons. not enough seats will be available.