STAT
Practice Final Exam Solns AU10

# Write down the probability distribution for x

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who are in favor of casinos in Ohio. Write down the probability distribution for X. (Remember we discussed in lecture what a probability distribution is.) Binomial: n=2 p=0.3 k 0 1 2 P(X=k) 0.49 0.42 0.09 27. Suppose 85% of your employees got raises last year. You sample 100 employees at random and count the number who got a raise. What is the chance that at least 80 of the employees got a raise? Normal Approximation to the Binomial 10 85 85 . 0 100 = × = np 10 15 15 . 0 100 ) 1 ( = × = - p n 85 85 . 0 100 = × = = np X μ 571 . 3 75 . 12 15 . 0 85 . 0 100 ) 1 ( = = × × = - = p np X σ 40 . 1 571 . 3 85 80 - = - = - = σ μ X Z P(X > 80) = P(Z > -1.40) = 1 - 0.0808 = 0.9192 ANS__0.9192_____ 4

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28. Suppose a manufacturer has recorded its cost of electricity (in dollars) and the total number of hours of machine time for their factory during a certain number of weeks. Using this information, how much does the cost increase for each additional hour of machine time? (Use proper units.) Descriptive Statistics: Time, Cost Variable N Mean SE Mean StDev Variance Time 52 10.865 0.369 2.664 7.099 Cost 52 1041.9 35.9 258.9 67043.1 Pearson’s Correlation: 0.7375 Y – Cost X – Time hour s s r b X Y \$ 67 . 71 664 . 2 9 . 258 7375 . 0 = = = ANS____\$71.67 ______ 29. Let X = price of stocks in Bob’s portfolio; Mean of X = \$20, SD = \$5. After 6 months, suppose the price of all the stocks in Bob’s portfolio went down by 50%. a. What is the new mean of Bob’s stocks? 10 \$ 20 5 . 0 5 . 0 5 . 0 = × = = X X μ μ b. What is the new SD of Bob’s stocks? 50 . 2 \$ 5 5 . 0 5 . 0 5 . 0 = × = = X X σ σ 30. Suppose Bob estimated the average exam score for his large class by taking a random sample of 50 students. The margin of error for Bob’s 95% confidence interval was plus or minus 3 points. The mean of his sample was 82. What was the standard deviation of the population of exam scores assumed to be? 823 . 10 50 96 . 1 3 * = = = σ σ σ n Z MOE ANS_____10.823 ______ 5
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