Code 1051 Suppose the random variable has pdf given by the following function

Problem Code: 1051Suppose the random variable has pdf given by the following function:Part a:Find the value of that makes a valid density function.Part b:Find Part c:Find Part d:Find the value of csuch that Xf(x) =⎧⎩⎨⎪⎪38x200≤x≤aotherwiseafP(X≤1)P(X≥1)P(X≤c) = 0.05 . Part e: Find . a) I have placed my work and my answer on my answer sheet. b) I want to have points deducted from my test for not working this problem. Question 11 Your answer is CORRECT. This is a written question, worth 20 points. DO NOT place the problem code on the answer sheet. A proctor will fill this out after exam submission. Show all steps (work) on your answer sheet for full credit. Problem Code: 1114 E ( X )

7/27/16, 12 : 36 PM Print Test Page 6 of 6 Part a:Let Z be the standard normal random variable. Calculate the following and draw a pictureillustrating each probability.(i) (ii) (iii) Find csuch that Part b:The weights of individual bolts produced at a manufacturing plant, , is normally distributed. Ifthe mean weight of the bolts is 9 grams and the standard deviation is 2.4 grams, find:(i) (ii)(iii) The value of such that Part c:Using the information from part b, if we randomly sample 61 weights and determine the samplemean, what is the probability that(i) The sample mean is less than 8.6 grams. (ii) The sample mean is at least 10.2 grams.P(∣Z∣ ≤0.9) =P(Z≥ −1.7) =P(Z≥c) = 0.62XP(X≤10.1)P(X≥7.3)xP(X≤x) = 0.95 a) I have placed my work and my answer on my answer sheet.b) I want to have points deducted from my test for not working this problem.