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[answered] 1. A key shop advertises that the keys made there have a P


A key shop advertises that the keys made there have a P = 0.75 of working effectively. If you bought 12 keys from the shop, what is the probability that all of the keys would work effectively?A student is taking a true/false exam with 13 questions. If he guesses on each question, what is the probability he will get at least 10questions correct?

A?student?is?taking?a?multiple-choice?exam?with?15?questions.??Each?question?has?five?alternatives.?If?the??student?guesses?on?11?of?the?questions,?what?is?the?probability??she?will?guess?at?least?6?correct??Assume?all?of?the?alternatives?are??equally?likely?for?each?question?on?which?the?student?guesses.You are interested in determining whether a particular child can discriminate the color green from blue. Therefore, you show the child tenwooden blocks. The blocks are identical except that nine are green and one are blue. You randomly arrange the blocks in a row and ask him to pick out a green block. After a block is picked, you replace it and randomize the order of the blocks once more. Then you again ask him to pick out a green block. This procedure is repeated until the child has made 14 selections. If he really can't discriminate green from blue, what is the probability he will pick a green block at least 12 times?

1. A key shop advertises that the keys made there have a P = 0.75 of working

 

effectively. If you bought 12 keys from the shop, what is the probability that all of the

 

keys would work effectively? 2. A student is taking a true/false exam with 13 questions. If he guesses on each

 

question, what is the probability he will get at least 10questions correct? 3. A student is taking a multiple-choice exam with 15 questions. Each question

 

has five alternatives. If the student guesses on 11 of the questions, what is the

 

probability she will guess at least 6 correct? Assume all of the alternatives are equally

 

likely for each question on which the student guesses. 4. You are interested in determining whether a particular child can discriminate the

 

color green from blue. Therefore, you show the child tenwooden blocks. The blocks

 

are identical except that nine are green and one are blue. You randomly arrange the

 

blocks in a row and ask him to pick out a green block. After a block is picked, you

 

replace it and randomize the order of the blocks once more. Then you again ask him

 

to pick out a green block. This procedure is repeated until the child has

 

made 14 selections. If he really can't discriminate green from blue, what is the

 

probability he will pick a green block at least 12 times? 5. A manufacturer of valves admits that its quality control has gone radically "downhill"

 

such that currently the probability of producing a defective valve is 0.4. If it

 

manufactures 1 million valves in a month and you randomly sample from these

 

valves 10,000 samples, each composed of 15 valves,

 

6. (a) In how many samples would you expect to find exactly 12 good valves?

 

(b) In how many samples would you expect to find at least 12 good valves? 7. Assume that 15% of the population is left-handed and the remainder is right-handed

 

(there are no ambidextrous individuals). If you stop the next nine people you meet,

 

what is the probability of the following situations? For the purposes of this problem,

 

assume independence in the selection of the nine individuals.

 

(a) all will be left-handed

 

(b) all will be right-handed

 

(c) exactly four will be left-handed

 

(d) at least three will be left-handed 8. In your voting district, 45% of the voters are against a particular bill and the rest

 

favor it. If you randomly poll five voters from your district, what is the probability thatNineteen students living in a college dormitory participated in a taste contest

 

between the two leading colas.

 

(b) If there really is no preference, what is the probability that at least 15 would

 

prefer Brand X to Brand Y?

 

(c) How many of the 19 students would have to prefer Brand X before you would be

 

willing to conclude that there really is a preference for Brand X?

 

at least 9. In a binomial situation, if P = 0.22, Q =

 

10. Twenty-eight biased coins are flipped once. The coins are weighted so that the

 

probability of a head with any coin is 0.45. What is the probability of getting at

 

least 16 heads?

 


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