Trevor is interested in purchasing the local hardware/sporting goods store in th
ID: 3339866 • 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 65% 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.) at least 6 out of 10 business day (c) fewer than 5 out of 10 business days (d) fewer than 6 out of the next 20 business days
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
(a)at least 6 out of 10 business day
Sol: given n=10
p=0.65
x=6
=10C6*(0.65)6*(0.35)4 + 10C7*0.657*0.353 + 10C8*0.658*0.352 + 10C9*0.659*0.351 + 10C10*0.6510*0.350
=(210)*0.0754*0.0150+120*0.0490*0.0428+45*0.0318*0.1225+10*0.0207*0.35+0.0134
=0.23751+0.2516+0.1752+0.0724+0.0134
=0.75011
(c) fewer than 5 out of 10 business days
Sol:given n=10
p=0.65
=10C4*0.654*0.356 + 10C3*0.653*0.357 + 10C2*0.652*0.358 + 10C1*0.651*0.359 + 10C0*0.650*0.3510
=210*0.1785*0.0018+120*0.2746*0.0006+45*0.4225*0.0002+10*0.65*0.00007+0.00002
=0.0067+0.0119+0.0038+0.0004+0.00002
=0.0228
(d) fewer than 6 out of the next 20 business days
Sol:20C5*0.655*0.3515 + 20C4*0.654*0.3516 + 20C3*0.653*0.3517 + 20C2*0.652*0.3518 + 20C1*0.651*0.3519 + 20C0*0.650*0.3520
(e) more than 17 out of the next 20 business days
sol:20C20*0.6520*0.350 + 20C19*0.6519*0.351 + 20C18*0.6518*0.352
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