Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
STP 226 NAME: Fall 2000 ID: Exam #2C Key This is a closed book exam. You may use a calculator and a formula page from the book. 1. Given P(A) = 0.7 and P(notB) = 0.6 and P(AorB) = 0.8 a) (5 points) compute P(B) P(B)=1-.6=.4 b) (6 points) Compute P (A&B). .8 = .7 + .4 -P(A&B), P(A&B) = .3 2. Toss a fair coin twice. a) (5 points) Let A=first toss came up heads. List outcomes in A. A={ htt, hht, hth, hhh} b) (6 points) What is the probability that first toss is not a head? P(notA) = 1 - 4/8 =.5 3. A frequency distribution for the number of siblings of 45 students in one of the STP 226 classes is given in the table below: Number of 0 1 2 3 4 5 6 7 siblings Number of 7 6 12 8 5 4 2 1 students (frequency) For a student selected at random from that class, let A= event that student has at most 2 siblings B= event that student has at least 5 siblings a. (7 points) Compute P(AorB) 32/45 = .711 b. ( 6 points) Are events A , B mutually exclusive? Clearly explain why or why not? Yes, there are no common outcomes. 4. Use the standard normal curve to find the following: a. (7 points) area between - 1.82 and 1.78 Area left of 1.78 - area left of -1.82 = .9625 - .0344 = .9281 b. (7 points) z-value with the area equal to 0.004 to the left of it. Z= -2.65 5. The lifetime of a particular brand of fuse is normally distributed with mean = 1600 hours and standard deviation = 50 hours. Let X be the lifetime of randomly selected fuse of that brand. a. (7 points) Sketch the distribution of that population and point out all of its main features (shape, center, spread) Bell shaped curve, symmetric,centered at 1600, most area between 1450 and 1750, total area=1 b. (7 points) Determine the following probability: P(X < 1680)= P(z < (1680-1600)/50) = P(z < 1.6) = .9452 b. (8 points) Derermine the 90th percentile of the distribution of X . 90th percentile of N(0, 1) is z=1.28. (area to the right of z=1.28 is 10 %) x=+z, so x=1600+1.28(50) =1664 6. A random sample of size 25 was taken from the normally distributed population with mean = 150 and standard deviation =20 . Let x denote the mean of this sample. a. (6 points) Name the sampling distribution of x , give the mean and the standard deviation of x . Normal distribution x =150, x =4 N(150,4) b. (7 points)Compute the probability that x is less than 153: P ( x < 153) =P(z< (53-150)/4) = P(z<.75) = .7734 7. You want to estimate the true mean weight of all the students at the large university ( ) A random sample of n = 9 students gives a sample mean of 145 lb. Assume that the weights of the students at that university are normally distributed with standard deviation of 18 lb. a. (6 points) Obtain 90% confidence interval for , the true mean weight. Z-interval, since is known 145+/- 1.645(18/3) gives (135.13, 154.87) b. (5points)Looking at your interval, is the true mean likely to be = 153 lb.? Clearly explain your answer. Yes, since clearly 153 is in the interval and we have 90% confidence that this interval captures the true mean. c. (5points)What sample size do you need so that your confidence interval has a margin of error of no more than 4 lb. (keep the same 90% confidence level). n=[(1.6458*18)/4]2 =54.79 ~ 55