Trevor is interested in purchasing the local hardware/sporting goods store in th
ID: 3132842 • Letter: T
Question
Trevor is interested in purchasing the local hardware/sporting goods store in the small town of Dove Creek, Montana. After examining accounting records for the past several years, he found that the store has been grossing over $850 per day about 70% of the business days it is open. Estimate the probability that the store will gross over $850 for the following. (Round your answers to three decimal places.)
(a) at least 3 out of 5 business days
(b) at least 6 out of 10 business days
(c) fewer than 5 out of 10 business days
(d) fewer than 6 out of the next 20 business days
(e) more than 17 out of the next 20 business days
Explanation / Answer
The random variable X= the store will gross over $850 follows binomial distribution with p=0.70
(a)Pr(at least 3 out of 5 business days)
=P(X>=3)
=5C3*0.70^3*0.30^2
=0.836
(b) Pr(at least 6 out of 10 business days)
=P(X>=6)
=10C6*0.70^6*0.30^4
=0.849
(c)Pr(X<5)
=10C0*0.70^0*0.30^10+…+10C4*0.70^4*0.30^6
=0.047
(d)P(X<6)
=10C0*0.70^0*0.30^10+…+10C5*0.70^5*0.30^5
=0.00004
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