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1 MATH 1342ÞP04 FALL 2010 CHAPTERS 4, 5 & 6 NAME SHOW ALL WORK FOR CREDIT!!! 1. A study was done to investigate a possible relationship the circumference (in ft) and the height (in ft) of trees. The data collected from nine trees in Marshall, Minnesota is given below. Circumference (ft) Height (ft) a. Determine the linear correlation coefficient between circumference and the height. b. Find the least-squares regression line, treating the circumference as the explanatory variable ( B) and height as the response variable ( CÑÞ c. Suppose a tree has a circumference of 4.5 ft, use the least-squares prediction line to predict the height of the tree.
2 MATH 1342.P04 PAGE 2 2. The following probability model shows the distribution of doctoral degrees from U.S. universities in 2005 by area of study. Area of Study Probability Engineering!Þ"%) Physical Sciences!Þ"!! Life Sciences!Þ"(" Mathematics!Þ!#) Computer Sciences!Þ!#' Social Sciences Humanities Education Professional and other fields!þ"(#!þ""%!þ"%%!þ!*( a. What is the probability that a randomly selected doctoral candidate who earned a degree in 2005 studied mathematics? b. What is the probability that a randomly selected doctoral candidate who earned a degree in 2005 studied humanities or social sciences? 3. The probability that a randomly selected 59-year-old male will live to be 60 years old is!þ*)*#&, according to the National Vital Statistics Report, Vol. 58, No. 10. a. What is the probability that two randomly selected 59-year-old males will live to be 51 years old? b. What is the probability that at least one of three randomly selected 59-year-old males will not live to be 60 years old?
3 MATH 1342.P04 PAGE 3 4. The following table represents the employment status and gender of the civilian labor for ages 16 to 24 (in millions). Male Female Total Employed Unemployed Total a. What is the probability that a randomly selected 16- to 24 year old individual from the labor force is unemployed and male? b. What is the probability that a randomly selected 16- to 24 year old individual from the labor force is employed or female? c. What is the probability that a randomly selected 16- to 24 year old individual from the labor force is female given that they were employed? 5. To play the Cash Five Lottery you pick 5 numbers from 1 to 37. a. How many different ways are there to pick 5 numbers? b. If you match 4 of the 5 winning numbers in Cash Five you win $472. How many ways can you match 4 of the 5 winning numbers?
4 MATH 1342.P04 PAGE 4 6. A security code consists of two letters followed by three digits 0 through 9. How many codes are possible? 7. A family has six children. If this family has four girls and two boys, how many different birth and gender orders are possible? 8. Determine whether the following distribution is a discrete probability distribution. If not, state why. B T B!!Þ!"& "!!Þ#$) #!!Þ$(% $!!Þ$%" %!!Þ!)& 9. Three males with an X-linked genetic disorder have one child each. In the following probability distribution, the random variable \ is the number of children among the three who inherit the X-linked genetic disorder. Compute the mean, variance, and standard deviation of the random variable \. B T B!!Þ%#"* "!Þ%#"* #!Þ"%!' $!Þ!"&'
5 MATH 1342.P04 PAGE Clarinex-D is a medication whose purpose is to reduce the symptoms associated with a variety of allergies. In clinical trials of Clarinex-D, 5% of the patients in the study experienced insomnia as a side effect. A random sample of 20 Clarinex-D users is obtained, and the number of patents who experienced insomnia is recorded. a. Find the probability that exactly 6 experienced insomnia as a side effect. b. Find the probability that 10 or fewer experienced insomnia as a side effect. c. Find the probability that 8 or more experienced insomnia as a side effect. d. Calculate the mean and standard deviation for the number of users a sample of 20 that would experience insomnia as a side effect.
6 MATH 1342.P04 PAGE 6 Formulas and Rules For any event I, - T I œ " T I If E and F are mutually exclusive events, then T E or F œ T E T F If E and F are not mutually exclusive events, then T E or F œ T E T F T E and F If E and F are independent events, then T E and F œ T E T F If E and F are dependent events, then T E and F œ T E T FlE If E and F are two events, then T FlE œ T E and F T E Permutations with Nondistinct Items The number of permutations of 8 objects of which 8" are of one kind, 8# are of a second th kind,..., and 85 are of the 5 kind is given by 8x 8x " 8x # â 8x 5 Frequency Distributions Binomial Distribution TI-Calculator. œ # D D B TÐBÑ 5 œ B. TÐBÑ #. œ8 : 5 œè8 : ; T \ œ B œ binompdf 8, :, B T \ Ÿ B œ binomcdf 8, :, B
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