8. The probability of a randomly selected adult in one country being infected wi
ID: 3043368 • Letter: 8
Question
8. The probability of a randomly selected adult in one country being infected with a certain virus is
0.003. In tests for the virus, blood samples from 20 people are combined. What is the probability that the combined sample tests positive for the virus? Is it unlikely for such a combined sample to test positive? Note that the combined sample tests positive if at least one person has the virus.
The probability that the combined sample will test positive is
.(Round to three decimal places as needed.)Is it unlikely for such a combined sample to testpositive?
A.
It
is not unlikely for such a combined sample to test positive, because the probability that the combined sample will test positive is greater than 0.05.
B.
It
Is unlikely for such a combined sample to test positive, because the probability that the combined sample will test positive is less than or equal to less than or equal to than 0.05.
C.
It
is not unlikely for such a combined sample to test positive, because the probability that the combined sample will test positive is less than or equal to Less than or equal to than 0.05.
D.
It
Is unlikely for such a combined sample to test positive, because the probability that the combined sample will test positive is greater than 0.05.
9.
A pharmaceutical company receives large shipments of aspirin tablets. The acceptance sampling plan is to randomly select and test 60 tablets, then accept the whole batch if there is only one or none thatdoesn’t meet the required specifications. If one shipment of 7000 aspirin tablets actually has a
4% rate ofdefects, what is the probability that this whole shipment will beaccepted? Will almost all such shipments be accepted, or will many be rejected?
The probability that this whole shipment will be accepted is
.
(Round to four decimal places as needed.)
The company will accept
nothing%
of the shipments and will reject
nothing%
of the shipments, so
(Round to two decimal places as needed.)
10. When purchasing bulk orders of batteries, a toy manufacturer uses this acceptance sampling plan: Randomly select and test 52 batteries and determine whether each is within specifications. The entire shipment is accepted if at most 3 batteries do not meet specifications. A shipment contains 3000 batteries, and 3% of them do not meet specifications. What is the probability that this whole shipment will be accepted? Will almost all such shipments be accepted, or will many be rejected?
The probability that this whole shipment will be accepted is
.
(Round to four decimal places as needed.)
The company will accept
nothing%
of the shipments and will reject
nothing%
of the shipments, so
many of the shipments will be rejected.
almost all of the shipments will be accepted.
(Round to two decimal places as needed.)
The probability is
Explanation / Answer
Solution
(8) Given that p = 0.003
and n = 20
P(combined sample test to be positive) = 0.003*20 = 0.06
P(X>=1) =1- P(X=0) = 1- (1-0.003)20 = 0.0583
It is not unlikely for such a combined sample to test positive, because the probability that the combined sample will test positive is greater than 0.05.
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