Matt Jones Math 1530 Elements of Statistics Exam II NAME Take the class period to complete this exam You may use a calculator a writing utensil one page of notes normal tables and your brain Do not share any materials and must do your own work to receive any credit Good luck 1 Shade the appropriate regions in the following Venn diagrams 2 How many ways can you choose five CDs from ten to take on a trip 3 How ways can you choose five CDs from ten and listen to them in order 4 The results of a recent poll of 794 people on how to deal with an energy shortage are below Response Frequency More conservation 302 More production 355 Both 98 No opinion 39 Total 794 a What is the probability that a person chosen at random responded More conservation b What is the probability that a person chosen at random responded Both or No opinion 5 Suppose X has a normal distribution with mean 52 and standard deviation 2 5 Calculate a P X 55 5 b Calculate P 51 X 56 c If a random sample of size 10 is taken from this distribution what is the chance its mean will be more than 0 3 from 52 6 What is the approximate distribution of the mean of a random sample of size 55 from a population whose mean and standard deviation are 39 and 2 respectively 7 Calculate a z0 06 b z0 87 8 The air pressures in tires of automobiles in the parking lot are distributed approximately normal with mean 29 6 psi and standard deviation 1 8 psi What is the 92nd percentile 9 The data corresponding to the following normal probability plot are likely to be coming from a normal distribution TRUE FALSE 10 An engineer chooses twelve switches from a large shipment you may assume the shipment size is infinite Unknown to the engineer 5 of the switches are bad What is a the probability that exactly two of the twelve switches are bad b the probability that at least one of the twelve switches is bad c the expected number of the twelve switches that are bad d the standard deviation of the number of the twelve switches that are bad 11 The number of siblings X that a person has is a random variable with distribution as indicated by the following histogram a What is the probability a person chosen at random from this group will have at least three siblings b What is the average number of siblings for people from this group c What is the standard deviation of the number of siblings for people from this group
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