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 If the outcome described in part (d) actually occurred, might it shake your confidence in the statement p = 0.70? Might it make you suspect that p is less than 0.70? Explain.

Yes. This is unlikely to 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.

No. This is unlikely to happen if the true value of p is 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 (e) 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.

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 of p is 0.70.

No. This is likely to happen if the true value of p is 0.70.

Answer 1

a)

here this is binomial with parameter n=5 and p=0.7

P(X>=3)=1-P(X<=2)=

1-∑x=0x-1   (nCx)px(q)(n-x) =

0.837

b)

P(X>=6)=1-P(X<=5)=

1-∑x=0x-1   (nCx)px(q)(n-x) =

0.850

c)

P(X<=4)=

∑x=0a     (nCx)px(1−p)(n-x)    =

0.832

d)

P(X<6)=

∑x=0a     (nCx)px(1−p)(n-x)    =

0.000

Yes. This is unlikely to happen if the true value of p is 0.70

e)

P(X>17)=1-P(X<=17)=

1-∑x=0x-1   (nCx)px(q)(n-x) =

0.035

Yes. This is unlikely to happen if the true value of p is 0.70.