Trevor is interested in purchasing the local hardware/sporting goods store in th

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 su50 per day about /0% of the business days it is open. Estimate the probability that the store wil gross over $ 5 r ie owing Round your answer to re dec malpace (a) at least 3 out of 5 business days (b) at least out of 10 business days (c) fewer than S out of 10 buslness days (d) fewer than 6 out of the next 20 business day:s Enter a number If the outcome described in part (d) actually occurred, might it shake your confidence in the statement -0.107 Might it make you suspect that is less than U.10? Lxplain. O Yes. This is unlikely Lo happen if the true value of p is 0.70. Yes. This Is likely to happen If the true value of p is 0.70. O No. This ls unlikely to happen if the true value of ls 0.70. No. This is likely to happen if the true value of p is 0.70. e) more than 17 out of the next 20 business days If the outcome described in part () actually occurred, might you suspect that p is greater than 0.70? Explain. Yes. This is unlikely to happen if the true value of p is 0.70. O Yes. This is likely to happen if the true value of p is 0.70 No. This is unlikely to happen if the true value ot p is 0.70 No. This Is likely to happen If the true value of p Is 0.70.

Explanation / Answer

As per binomial distribution,
P(X=r) = nCr * p^r * (1-p)^(n-r)

p=0.7

a)
P(X >= 3) = 0.8369 (Excel formula used =1 - BINOM.DIST(2,5,0.7,TRUE))

b)
P(X >= 6) = 0.8497 (Excel formula used =1 - BINOM.DIST(5,10,0.7,TRUE))

c)
P(X < 5) = 0.0473 (Excel formula used =1 - BINOM.DIST(4,10,0.7,TRUE))

d)
P(X < 6) = 0.000043 (Excel formula used =BINOM.DIST(5,20,0.7,TRUE))

Yes, this is unlikely to happen if the true value of p is 0.70

e)
P(X > 17) = 0.0355 (Excel formula used =1-BINOM.DIST(17,20,0.7,TRUE))

Yes, this is unlikely to happen if the true value of p is 0.70

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