1.Findthe probabilities for the following discrete random variables a.Amonga shipment of 5,000 tires, 1,000 are slightly blemished.If one purchases 10 of these tires, what isthe probability that...

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1. Find the probabilities for the following discrete random variables


a. Among a shipment of 5,000 tires, 1,000 are slightly blemished.If one purchases 10 of these tires, what is the probability that 3 or less (P (x


b.The probability that a hockey game will go into overtime is .3; Of the next 12 hockey games, what is the probability that more than 3 (P(x >3)) will go into overtime?


c.The probability that a person, living in a certain city, owns a dog is estimated to be 0.3.Find the probability that the tenth person randomly interviewed in that city is the sixth one to own a dog.


d.A local drugstore owner knows that, on average, 100 people per hour stop by his store. Find the probability that in a given 3 minute period, more than 5 (P(x > 5) people enter the store.


e.An electronic switching device occasionally malfunctions and may need to be replaced.It is known that the device is satisfactory if it makes, on average no more than .2 errors per hour.A particular five hour period is chosen as a “test” on the device. If no more than 1 error occurs, the device is considered satisfactory.What is the probability that a satisfactory device will be mis- diagnosed as “unsatisfactory” on the basis of the test?


f.A restaurant chef prepares a tossed salad containing, on average, 5 vegetables per day.Find the probability that the salad contains more than 5 vegetables on i) a given day and on ii)3 of the next 4 days?



Answered Same DayDec 20, 2021

Answer To: 1.Findthe probabilities for the following discrete random variables a.Amonga shipment of 5,000...

David answered on Dec 20 2021
127 Votes
4 1. Find the probabilities for the following discrete random variables
a. Among a shipment of 5,000 tires,
1,000 are slightly blemished. If one purchases 10 of
these tires, what is the probability that 3 or less (P (x <= 3) are blemished?
Solution: let X=number of blemished tires
This is a hyper geometric problem
( ) ∑(


)
(


) (


)
Time consuming and messy to compute, but since N=5000 is much greater than n=10, we
can use the binomial approximation, with prob of blemish p=1000/5000=0.2 and sample size
n=10
( ) ∑(


)
( ) ( )
b. The probability that a hockey game will go into overtime is .3; Of the next 12 hockey
games, what is the probability that more than 3 (P(x >3)) will go into overtime?
Solution: Binomial Problem with n = 12 and p(overtime) = 0.3
P(4<= x <=12) = 1 - P(0<= x <=3) = 1 – binom cdf(12,0.3,3)
= 1 - 0.4925
= 0.5075
c. The probability...
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