18. Question Details My Notes Ask Your Teacher Trevor is interested in purchasin

Question

18. Question Details My Notes Ask Your Teacher 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 50% 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 If the outcome described in part (d) actually occurred, might it shake your confidence in the statement p 0.50? Might it make you suspect that p is less than 0.50? Explain Yes. This is unlikely to happen if the true value of p is 0.50. Yes. This is likely to happen if the true value of p is 0.50 No. This is unlikely to happen if the true value of p is 0.50 No. This is likely to happen if the true value of p is 0.50 (e) more than 17 out of the next 20 business days If the outcome described in part (e) actually occurred, might you suspect that p is greater than 0.50? Explain Yes. This is unlikely to happen if the true value of p is 0.50 Yes. This is likely to happen if the true value of p is 0.50 No. This is unlikely to happen if the true value of p is 0.50 No. This is likely to happen if the true value of p is 0.50

Explanation / Answer

We will use the binomial pdf formula to solve the problem:

P(n,x,p) = nCx (p^x)*(1-p)^(n-x). We will use it to solve every problem below.

p = .50

a. at least 3 out of 5 business days

P(X>=3) = P(X=3,4,5) = .50
b. at least 6 out of 10 business days

P(X>=6,7,8,9,10) = P(X=6)+P(X=7)+P(X=8)+P(X=9)+P(X=10)

= 0.377
c. fewer than 5 out of 10 business days

P(X<5) = P(X=0,1,2,3,4) = 0.377

d. fewer than 6 outof the next 20 business days. If thisactually happened might it shake your confidence inthe statementp=0.50? Might it make you suspect that p is less than 0.50?Explain.

P(X<6) =P(X=0,1,2,3,4,5) = 0.0207 or .021

No, the probability of X<6 event happening is just low. and I am not surprised inspite of having p = .50

e. more than 17 out of the next 20 business days. Ifthis accually happened might you suspect that p is greater than0.60? Explain.

P(X>17) = P(X=18,19,20) = 0.0002 or .000
Again, this is not a surprise, X>17 is a pretty rare event and thus .000 is kinda expected

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