2. Now evaluate an exponential probability distribution for the lifetime data. Recall that the exponential pdf is f(y) = -/B In the last column of the table on the previous page, find the expected ith observations for an Exponential with = 1. With = 1, the pdf is f(y) = ex. So for each value of p, you must find the value of Q so that fo e-* dx = p. Luckily, this has a nice closed form solution Q = -In(1 - p) Plot the new (X, Y) pairs. 3.0 2.5 2.0 Probability Plot of Lifetime Exponential Score 1.5 10 0.5 0.0 05 10 15 20 25 30 35 Lifetime 3. Which probability model is a better fit for the lifetime data - the normal or exponential? EXPLAIN. Part II 1. A researcher is attempting to determine an appropriate probability distribution for a set of data that she has collected. A. Which distribution the data being compared to in the plot to the right? B. Examine the pattern of the points in the plot to the right, Does it appear that the probability model identified in part A is appropriate for this data? EXPLAIN. 2015 20. 15 2.5 20 Probability Plot of X Gamma 1 X Scrire 0. Score Scure 2. Enhanced probability plots - like those below - have "confidence bands". For a probability model to be appropriate, almost all points should be within the confidence bands. Complete the sentences to provide an explanation of what each probability plot below is indicating. Probability Plot of A Normal 45% CL 11 + 13 14 Probability Plot of B Exponential -55% C The 10 100 1000 Probability Plot of C Normal-45% CL The The probability distribution (circle one) IS/IS NOT appropriate for data set A because probability distribution (circle one) IS/IS NOT appropriate for data set B because probability distribution (circle one) IS/IS NOT appropriate for data set C because Part III Researchers recorded the length of time (in seconds) that a user views a page on a web site before moving to another page for a random sample of web page "views". Using the MINITAB statistical software, we can create a set of probability plots to evaluate many distributions at once. Open Minitab. Werlhes: 1 T** c1 C2 C ' View Time 085 2 1.58 3 27 4 2.00 5 356 1.29 5.11 8 6.10 Enter the data into column C1 and name it "View Time" 9 7.43 10 11 W www 142 n Ven Tire 14 224 3 320 " 426 Rey Multiv TimeS Lelles N B 12 . 14 that Choose Stat Quality Tools Individual Distribution Identification Enter "View Time" as a Single column of data and the subgroup size as 1. Select "Specify" for the distributions. ary Cpy Sp | Unasz stand: (Rared D Thorardi (Rev L Individud Leiden efte LUK area is |* Sn@2xkm's ||New mel BOX L04.. The Accept Samping by Va tural Syyt Used | (by Manba: Ma Gr Farba: Wet hd 4: eme Octions. Carcel In each plot, look to see if the data is approximately a straight line, and whether almost all the points are between the confidence bands. Based on the set of probability plots, which probability distribution do you think is most appropriate for the web page view times? EXPLAIN. Part I The lifetimes (in 100 hours) for a random sample of a new brand of light bulbs are given below. 15.0 1.4 12.3 1.0 9.2 7.6 34.6 1. Construct a normal probability model for the lifetimes of the lightbulbs. First, fill in the table. Then, draw the probability plot by plotting the (X, Y) pairs. 4.2 Ordered value of Place in (i-0.5) ordered p= Find expected ith observation from the NORMAL distribution Save this (X, Y) pair column for data n list [0] Question 2 Q 1.0 1 0.0625 -1.53 (1.0, -1.53) 0.06 Score -1 2 1 Probability Plot of Lifetime Normal -2 5 10 15 20 25 30 35 Lifetime