Chapter 6: Normal Probability (These problems are like theproblems in Section 6.2). Using a Normal Distribution to findprobabilities: Use the table E.2 in your text. Draw a sketch andindicate what probabilities (E.g. P (X<3 and X>10) for whatis required for each part of the problem. To make sketches copy andpaste into Word for the areas under the bell-curve you have theNormalSketch.ppt powerpoint slide in the Resources ? Handout areaon Laulima, The main point of providing a sketch is to give you avisual idea of what your solution will be. 2. Do problem (6 points)Remember, you need the sketches to get credit. You order and managethe medications in the Pharamacy for Queens hospital. The CEO isconcerned because the hospital is ordering and stocking medicinewith short shelf lives and its not being used and thrown away.There is a medicine called Harvoni that is used for Hepatitis thecost of a treatment is $95,000 and the shelf life for the medicineis 12 weeks. Last year s significant amount of this medicine wasdisposed because of the short shelf life: How many treatmentsshould you order? For this question the mean (?) was 20, thestandard deviation (?) was 5, skewness was .06 and kurtosis was -.27. a. You can find the probabilities for this problem assuming anormal (bell-shaped) curve. Why is it OK for this particularsituation? b. What is the probability that you will use no morethan10 treatments in a given week? c. What is the probability thatwill use more than 36 treatments in a given week? d. Would usingmore than 36 treatments in a week be an outlier for this data set?e. You expect touse ? harvoni each day. Because of the variabilityyou will actually sell more or less each day. To understand this,find out how many less or more than ? you expect to sell 80% of thetime. That is, find two values equal distance from the mean suchthat 80% of all values fall between them. Specifically find whatnumber of x Harvoni where 80% of the values fall between ?-x and?+x f. You can only have a fixed amount of amount of treatments onhand to sell every week. As in (e) you know you will surely usemore or less than ? treatments each week. If you run out oftreatments, your patients will die. But if you order too manytreatments they will go bad and you will have to throw them out soyou are willing to sell out occasionally. How many treatments mustyou have on hand to sell if you wanted to ensure you do not runlout more than 5% of the time? (This is called having a 95% servicelevel) g. The z-value for having a given service level is calledthe safety-factor. Explain what this factor does in terms of ? and? for the 95% service level you found in (f). What if you wanted toonly have a 50% service level? What about 40% service level?
