STAT 2601 STATISTICAL METHODS INFORMATION ON THE SECOND MIDTERM EXAMINATION Date October 22 2010 Friday Time 9 15 10 20 Place SCI 3550 Examination Type Closed notes and books But you will be allowed to use one sheet of paper information sheet with the formulas and facts that you need This sheet should not have solutions of problems or examples The things that you need for the exam 1 A calculator with exponential key and or photocopy of Table V 2 Photocopies of Table II III and IV 3 Formula Handout Coverage Sections 4 1 6 3 included Previous exams On the course outline page at www morris umn edu sungurea introstat index2601 html Interactive practice test http umconnect umn edu p19098565 The important topics that you should know for the exam Chp 4 Discrete Random Variables 4 1 Types of random variables Discrete and Continuous 4 2 Probability distributions for discrete random variables Construction of a discrete probability distribution Finding probabilities by using a given probability distribution 4 3 Expected values of a discrete random variable Finding mean variance and standard deviation 4 4 The binomial random variable Verifying the characteristics of a binomial random variable The probability distribution of a binomial random variable The mean variance and standard deviation of a binomial random variable Finding probabilities related with the binomial distribution by using i Probability distribution p x ii Binomial Tables 4 5 The Poisson random variable Verifying the characteristics of a Poisson random variable The probability distribution of a Poisson random variable The mean variance and standard deviation of a Poisson random variable Finding probabilities related with the Poisson distribution by using Poisson probability distribution Poisson approximation to Binomial probabilities Chp 5 Continuous Random Variables 5 1 Continuous probability distribution 5 2 The uniform distribution The probability distribution of a uniform random variable on the interval c to d The mean and standard deviation of a uniform random variable Finding probabilities for the uniform distribution by calculating the areas of the rectangles 5 3 The normal distribution Finding probabilities for standard normal and general normal distribution Given probabilities finding x z quartiles etc Use of Normal Table 5 4 Normal approximation to the binomial distribution Steps 1 4 on pages 215 5 5 The exponential distribution The probability distribution of an exponential random variable The mean and standard deviation of an exponential random variable Finding the Area A to the right of a number a for an exponential distribution SOLVING PROBLEMS WHICH INVOLVES MORE THAN ONE PROBABILITY DISTRIBUTION Chp 6 Sampling Distributions The difference between parameter and statistics 6 1 Sampling distribution Finding sampling distribution of a statistics Finding the mean and standard deviation of a sampling distribution 6 2 Properties of sampling distribution Point estimator Unbiased estimate Biased estimate Minimum variance estimator 6 3 Central Limit Theorem CLT Sampling distribution of x The mean of x The standard deviation of x standard error Approximate distribution of the sample mean for large n CLT EXAM II STUDY QUESTIONS CHAPTER 4 1 An employee of a firm has an option to invest 1 000 in the company s bonds At the end of 1 year the company will buy back the bonds at a price determined by its profits for the year From the past years the company predicts it will buy the bonds back at the following prices with the associated probabilities x price paid for bonds x 0 500 1 000 1 500 2 000 p x 01 22 30 22 25 a What is the probability the employees will receive 1 000 or less for the investment b What is the expected price paid for the bonds c What is the employee s expected profit d Find the variance and standard deviation for this probability distribution 2 In a poll conducted by Parents magazine 60 of parents said they wished they had received more education Parents August 1988 A random sample of twenty parents is selected a What is the probability distribution of x the number of parents who hold this view in this sample Justify your answer b What is the expected number of parents who will hold this view in this sample What is the standard deviation of the random variable in part a c Find the probability that exactly 3 will not hold this view in the sample d Use the normal approximation to find P 6 x 9 3 A particular type of birth control pill is 90 effective A random sample of 20 persons is selected a What is the probability distribution of x the number of unplanned births for this sample Justify your answer b How many unplanned births would you expect in this sample What is the standard deviation of the random variable defined in part a c Find the probability that exactly 3 out of 20 will have unplanned births 4 Consider writing onto a computer disk and sending it through a certifier that counts the number of missing pulses Suppose this number X has a Poisson distribution with mean 0 2 Suggested in Average Sample Number for Semi Curtailed Sampling Using Poisson Distribution J Quality Technology 1993 a What is the probability that a disk has exactly one missing pulse b What is the probability that a disk has at least two missing pulses 5 For a recent period of 100 years there were 93 major earthquakes at least 6 0 on the Richter scale in the world based on data from the World Almanac and Book of Facts Assuming that the Poisson distribution is a suitable model a Find the mean number of major earthquakes per year and the standard deviation b Find the probability that the number of major earthquakes in a randomly selected year is 5 c Find the probability that the number of major earthquakes in a randomly selected year is at least 2 CHAPTER 5 6 6 The speeds of all cars traveling on a stretch of Interstate Highway I 95 are normally distributed with a mean of 68 miles per hour and a standard deviation of 3 miles a Find the percentage of travelers who are violating the 65 miles speed limit b If a police officer decides to give a ticket to the fastest 10 of the drivers what should be the minimum speed he would use to write a speeding ticket c If a random sample of 36 cars traveling on this highway has been selected what is the probability that their average speed will exceed the 65 miles speed limit 7 Based on the sample data collected in the Denver area Nicholas Kiefer 1985 found that in some cases the exponential