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- For the statistics test scores the mean is 63 and the standard deviation is 7.0 and for the biology test scores the mean is 23 and the standard deviation is 3.9. a) A student who took both tests scored a 69 on the statistics test and a 26 on the biology test. Transform each test score to a standard z-score and determine on which test the student had a better score. b) If a student who took both tests has a standard z-score of a -1.67 on the statistics test and a 2.05 on the biology test, find the students actual test scores.Q2) From past experience, it is known that the number of tickets purchased by a student standing in line at the ticket window for the football match of UCLA against USC follows a distribution that has mean u = 2.4 and standard deviation o = 2.0. Suppose that few hours before the start of one of these matches there are 100 eager students standing in line to purchase tickets. If only 250 tickets remain, what is the probability that all 100 students will be able to purchase the tickets they desire?Suppose that the lifetime of a component (in hours) is modeled with a Weibull distribution 4000. Determine the following in parts (a) and (b): with B 2 and 8 = = a P(X > 5000) b P(X> 8000|X > 3000) c Comment on the probabilities in the previous parts compared to the results for an expo- nential distribution.
- 6) Suppose the m.g.f. of the r.v. X is given below: MCA) = (uM/ R0) +(45 |no) exp (t) A(20/1201eapreb a) Find the mean and variance of X b) Find P(X>1)Show all work4. Suppose you are given the following information: = 49.6870 – 2.1586X; r2 = 0.9757 (0.7463) (0.12113) df=8 T= (66.578) (-17.821) p-value = (0.000) (0.000) a) Conduct a two tailed hypothesis test that: i) The intercept is 49 and the slope coefficient is -2, use 1% significance. ii) Confirm your deductions to 4(a) (i) using a confidence interval approach b) What does the r2 tell you? c) Perform a hypothesis using r2, such that p=D0, what do you conclude?
- 9. Let X be a random variable with expected value 2 and variance 3. Compute the following quantities: a) E(2X+3) b) Var (2X) c) Var (X+3)1)When can a Standard Deviation for set of 5 numbers be zero? In other words, what kind of relationship must exist among all numbers in order for Standard Deviation to be zero Hint: Standard Deviation E(X¡ - Mean)²/(n – 1)Assume the below life table was constructed from following individuals who were diagnosed with a slow-progressing form of prostate cancer and decided not to receive treatment of any form. Calculate the survival probability at year 1 using the Kaplan-Meir approach and interpret the results. Time in Years Number at Risk, Nt Number of Deaths, Dt Number Censored, Ct Survival Probability 0 20 1 1 20 3 2 17 1 3 16 2 1 A) The probability of surviving 1 year after being diagnosed with a slow-progressing form of prostate cancer is .85. B) The probability of surviving 1 year after being diagnosed with a slow-progressing form of prostate cancer is .85 for the individuals being followed in this study. C) The probability of surviving 1 year after being diagnosed with a slow-progressing form of prostate cancer is .85 for individuals who decided against all forms of treatment. D) The probability of surviving 1 year…
- 3. Suppose that X has an exponential distribution with a mean of 10. Determine the following: (a) P(X 15) (c) Compare the results in parts (a) and (b) and comment on the role of memoryless property.(c) A factory produces two types of artificial lamp A and B. The mean durability of artificial lamp A is 850 hours and its standard deviation is 40 hours. While, mean durability of artificial lamp B is 820 hours and its standard deviation is 60 hours. Find the probbality of 35 artificial lamp A will have mean durabilirty at least 25 hours more than 45 artificial lamp B.A beverage factory machine fills can with chocolate drink follows the normal distribution with amean weight of 155 grams and a standard deviation of 5 grams. 1) A can is selected at random. Find the probability that the can’s weight less than 165 grams.2) The company of this chocolate beverage decided to replace the filling machine if 12.3% of thecan is filled the minimum of x grams of chocolate drink. Find the value of x.