Question

Trevor is interested in purchasing the local hardware/sportinggoods store in that small town of Dove Creek, Montana. Afterexamining accounting records for the past several months he foundthat the store has been grossing over $850 per day about 60% of thebusiness days it is open.

Estimate the probability that the store will gross over $850

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 outof the next 20 business days. If thisactually happened might it shake your confidence inthe statementp=0.60? Might it make you suspect that p is less than 0.60?Explain.
e. more than 17 out of the next 20 business days. Ifthis accually happened might you suspect that p is greater than0.60? Explain.

Answer 1

a)=0.6826

b)=0.6331

c))=0.1662

d)0.0016

Explanation:

Binomial Distribution refers to the distribution in whereby only two possible outcomes. It takes place whether the event is happening or not happening , irrespective of the number of trials.

Given:

p = 0.6, q = 1 - p = 0.4

a)P(At least 3 out of 5 days) = P(3) + P(4) + P(5)

P(X≥3)=P(X=3)+P(X=4)+P(X=5)=5C3×0.63×0.45−3+5C4×0.64×0.45−4+5C5×0.65×0.45−5

10×0.63×0.45- 3+5×0.64×0.45 - 4+1×0.65×0.45 - 5

=0.6826

(b)P(At least 6 out of 10 days)

p(X = 6) + p(X = 7) + p(X = 8) + p(X = 9) + p(X = 10) =

0.2508 + 0.2150 + 0.1209 + 0.0403 + 0.0061 = 0.6331

(c)P(5 out of 10 days )

checking the binomial distribution table

p(X < 5) =

p(X = 0) + p(X = 1) + p(X = 2) + p(X = 3) + p(X = 4) =

0.0001 + 0.0016 + 0.0106 + 0.0425 + 0.1114 =0.1663

(d)

P(X<6)=0.0016

P(X<6)=0.0016

from answer from option D, it shows that there is 0.16% chance distribution from the 20 random sample,then it can be concluded that P<0.60