2. Suppose that snowfall in Indiana follows an exponentialdistribution with mean

Question

2. Suppose that snowfall in Indiana follows an exponentialdistribution with mean 15 inches per winter season.

(a) Find the probability that the snowfall will exceed 17 inchesin a specific winter.

(b) Find the probability that in four out of the next fivewinters the snowfall will be less than the mean.

3. Sales in a fast food restaurant are normally distributed withmean $42,000 and standard deviation $2,000 during a salesperiod. During a recent sales period, sales were reported toa local taxing authority to be $37,600. Should the taxingauthority be suspicious?

Explanation / Answer

a) this probability can be found using the complement of 17 orfewer inches falling (poissoncdf(15,17)=.7489. 1-that value willgive us the probability of more than 17 inches. 1-.7489 is .2511,or about 25.1% b)Assuming that each winter is independent, the probability ofthe winter being less than 15 inches is poissoncdf(15,15)=.568.Now, we can use the binomial distribution to find the probabilityof 4 out of 5 winters having less than that... binompdf(5,.568,4)=.2249, or about 22.5% c) the z-score for 37,600 is (37600-42000)/2000=-2.2 Theprobability of seeing that z-score or lower isnormcdf(-1000000000,-2.2)=.0139 or about 1.39%. I would be a little suspicious; that seemspretty low. c) the z-score for 37,600 is (37600-42000)/2000=-2.2 Theprobability of seeing that z-score or lower isnormcdf(-1000000000,-2.2)=.0139 or about 1.39%. I would be a little suspicious; that seemspretty low.

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.