Question

Chapter 6: Normal Probability (These problems are like the problems in Section 6.2). Using a Normal Distribution to find probabilities: Use the table E.2 in your text. Draw a sketch and indicate what probabilities (E.g. P (X<3 and X>10) for what is required for each part of the problem. To make sketches copy and paste into Word for the areas under the bell-curve you have the NormalSketch.ppt powerpoint slide in the Resources  Handout area on Laulima, The main point of providing a sketch is to give you a visual idea of what your solution will be. 2. Do problem (6 points) Remember, you need the sketches to get credit. You order and manage the medications in the Pharamacy for Queens hospital. The CEO is concerned because the hospital is ordering and stocking medicine with short shelf lives and its not being used and thrown away. There is a medicine called Harvoni that is used for Hepatitis the cost of a treatment is $95,000 and the shelf life for the medicine is 12 weeks. Last year s significant amount of this medicine was disposed because of the short shelf life: How many treatments should you order? For this question the mean (μ) was 20, the standard deviation (σ) was 5, skewness was .06 and kurtosis was - .27. a. You can find the probabilities for this problem assuming a normal (bell-shaped) curve. Why is it OK for this particular situation? b. What is the probability that you will use no more than10 treatments in a given week? c. What is the probability that will use more than 36 treatments in a given week? d. Would using more than 36 treatments in a week be an outlier for this data set? e. You expect touse μ harvoni each day. Because of the variability you will actually sell more or less each day. To understand this, find out how many less or more than μ you expect to sell 80% of the time. That is, find two values equal distance from the mean such that 80% of all values fall between them. Specifically find what number of x Harvoni where 80% of the values fall between μ-x and μ+x f. You can only have a fixed amount of amount of treatments on hand to sell every week. As in (e) you know you will surely use more or less than μ treatments each week. If you run out of treatments, your patients will die. But if you order too many treatments they will go bad and you will have to throw them out so you are willing to sell out occasionally. How many treatments must you have on hand to sell if you wanted to ensure you do not runl out more than 5% of the time? (This is called having a 95% service level) g. The z-value for having a given service level is called the safety-factor. Explain what this factor does in terms of μ and σ for the 95% service level you found in (f). What if you wanted to only have a 50% service level? What about 40% service level?

Answer 1

2. Do problem (6 points) Remember, you need the sketches to get credit. You order and manage the medications in the Pharamacy for Queens hospital. The CEO is concerned because the hospital is ordering and stocking medicine with short shelf lives and its not being used and thrown away. There is a medicine called Harvoni that is used for Hepatitis the cost of a treatment is $95,000 and the shelf life for the medicine is 12 weeks. Last year s significant amount of this medicine was disposed because of the short shelf life:

How many treatments should you order? For this question the mean (μ) was 20, the standard deviation (σ) was 5, skewness was .06 and kurtosis was - .27.

a. You can find the probabilities for this problem assuming a normal (bell-shaped) curve. Why is it OK for this particular situation?
If we look at the summary statistics we find the skewness is less than one and kurtosis(peakness) is close to zero.
Also when a large number of sample are taken from a population, by Central limit theroem we know that the mean of the sampling distribution is normally distributed.

b. What is the probability that you will use no more than10 treatments in a given week?

c. What is the probability that will use more than 36 treatments in a given week?

d. Would using more than 36 treatments in a week be an outlier for this data set?

Yes because the probability of taking more 36 treatments is almost zero.