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_NAME (5)MATH 104 TEST # 3 SECTION _____April 19,
_2001
_ـH(HHЫ443!#34/-6Z/ЫYour grades on three tests in finite mathematics are 76, 88 and 72. Your grade on the final exam will count twice as much as any one test grade in determining your average grade for the course. In order for your average grade for the course to be 82, what must your grade on the final exam must be? (5)____________A shop supervisor counted the number of accidents each week during a year. The frequency distribution is given below.*-6Z*Ыnumber of accidents number of during week occurrences_____________________________*-6 Z*Ы0201152103 44 343333333334ҫ3Determine the relative frequency distribution for the possible number of accidents during the week. (5)____________3Find the expected number of accidents during a week. (5)____________433333333#4ҫTwo people play a game. A single die is thrown. If the outcome is a 3, then A pays B $4. How much should B pay A when a 1, 2, 4, 5 or 6 is thrown so that A and B break even, on average, over many repetitions of the game? (5)____________
ـThe variance of a probability distribution (5)a) is large if the mean is largeb) is small if the mean is largec) is always smaller than the meand) has little practical valuee) is the square of the standard deviation____________Find the mean, variance, and standard deviation for the probability distribution below. (5)4-6Z4ЫÂk Pr(X = k) À0 .41 .22 .33 .1____________If X is a random variable such that E(X2) = 11/2 and % = 2, calculate
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In a large group we find that mens weights are normally distributed with % = 130 lbs. and
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_ = 15 lbs. Find the 21st percentile of mens weights. (5)____________The distribution, called a triangular distribution, for a continuous random variable X is given below.Suppose we are going to take a simple random sample of size 500 from this distribution. (5) Which of the following histograms best portrays the sampling distribution of
? Explain.A shipment of steel bars will be accepted if the mean breaking strength of a random sample of 10 steel bars is greater than 250 pounds per square inch. The model for breaking strength is normal with a mean of 260 and a standard deviation of 20. What is the probability that a shipment will be accepted? (5)____________
Suppose you are in charge of student ticket sales for a major college football team. From past experience, you know that the number of tickets purchased by a student standing in line at the ticket window has a distribution with a mean of 2.1 and a standard deviation of 2.0. For todays game there are 100 students standing in line to purchase tickets. If a total of 220 tickets remain, what is the probability that all 100 students will be able to purchase the tickets they desire? (5)____________The distribution of the number of barrels of oil produced by a certain oil well each day has a mean of 400 and a standard deviation of 75. 4#########4ҫ# Describe the sampling distribution of the mean number of barrels produced per day for samples of 40 production days. (5)#What is the probability that the sample mean will be greater than 425? (5)____________4########4ҫMarket researchers use the number of sentences per advertisement as a measure of readability for magazine advertisements. The following represents a random sample of the number of sentences found in 49 advertisements. Find a point estimate of the population mean %. (Note: The sum of the data is 610.) (5)$Ы9201816916169111322165186652517237109101051118189917131461112111561214114918121217____________Assume that the number of sentences per advertisement are normally distributed with a standard deviation of 7 sentences. Determine a 95.44% confidence interval for the mean number of sentences per advertisement based on the sample in problem 16. (5)I have not violated the Honor Code in any way with regard to this work.Signature