Stats 309 ICA 2

Stats 309 ICA 2 - MTHSC 309 ICA#2 Name(s Sect 1 The...

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Unformatted text preview: MTHSC 309 ICA #2 Name(s) Sect 1. The weighted average of the possible values that a random variable X can assume, where the weights are the probabilities of occurrence of those values, is referred to as the: a. variance b. standard deviation C? expected value . covariance 2. Which of the following is not a characteristic of a binomial experiment? a. There is a sequence of identical trials ® Each trial results in two or more outcomes. c. The trials are independent of each other. d. Probability of success p is the same from one trial to another. 3. Let X represent the number of times a student visits a bookstore in a 1-month period. Assume that the probability distribution of X is as follows: 0 1 2 3 0.15 0.25 0.40 0.20 a.» What is the expected lue and stimdard de iatiitgris distribution? gm: 01,451+ 3595 + gum + 30203 :2 am 01.10% we wow 311,101iei-05 <r= “034.95% b. What IS the proba ' that the student Visits ookstore at least once in a month >0<20=~flfil c. What is the probability that the student visits the bookstore at most twice in a month? “Mm-9) 4. Given a binomial random variable with n = 20 and p = 0.75, find the following probabilities. a. P(XZ 15) ~ \ ’ worrier (20,36, :0 | ma) W‘ b. P(X = 17) bmmpmao.160700.133?l c. P(IZSX<17) UMDMCLW(20‘5le ‘ bmm/icdf(20\vjf§i “d r | {$339 , Jun—— 5. A recent survey in Michigan revealed that 60% of the vehicles traveling on highways, where speed limits are posted at 70 miles per hour, were exceeding the limit. Suppose you randomly record the speeds of 100 vehicles traveling on US 131 where the speed limit is 70 miles per hour. Let X denote the number of vehicles that were exceeding the limit. Find the following probabilities: Q). and {)3 “12) P: . (00 a. P(X: 50) buxom 90 l? (100, M065) 7., b. P(40 EX: 50) bmomczli‘UDbybqed)“ btflOfl'tfd‘l’UbO, .lobiffi) : 6. The American Statistician (May 2001) published a study performed on female students who suffer from bulimia. Each student completed a questionnaire from which a “fear of negative evaluation” (FNE) score was produced. (The higher the score, the greater the fear of negative evaluation.) Suppose the FNE scores of bulimic students follow aistribution with mean 20 and standard deviation 5. Consider a random sample of 50 female students with bulimia. Draw a picture for full credit! a. What is the probability that the sample’E score is greater than 18.5? S HRMKSX :.qg301.5;l.flE3OI I p , , Z 2 £2. 2 :3. l 3 0‘1 r ""7 n (y (Y ( EC“ 3‘0. ' y/ 7M ’2. L) .. 9N1 O 2. b. What is the probability that the sample’sNE score is between 18 and 19? mum/J?) 2 Manama Ml ‘ M ii.“ ‘ \ r r __ a... em- W h s ., o I w \01 90 x noanfl‘FUElci. 30, /{5‘0) [.0463 l 033 4}“ b 2: c. What is the probability that a randomly selected female student with bulimia will have a FNE K than17? ‘ g ' : " i'” (mtvtOeAt.(/94.\a.w.63:1.99‘6l a.» o 2’ 7. A university mathematics department gives a freshman calculus examination that allows those who pass to receive college credit for calculus. Exam scores ar distributed with u = 35 and c = 4. a. What is the probability that a randomly selected studet takin this exam will receive a score of 40 or better? 31"“ PM 740) 1 '5 “ ' 3W“ Z 41 “‘1 M. Hart-wch (40.96533?) 91.10660) L36 . Z . . b. Wgat score Will be exceeded by 80% of the students taking this exam? £0 a. r ’o, M 5 ~34 :25 ’43 nx 0 e time requrred to complete a partlcular assembly operation 13 distributed between 25 and 50 minutes. a. What is the probability that the assembly operation will require more than 40 minutes to complete? Aabb :D (5%) 96 Lib 60 : or: |nuri01m(.1q3‘5, v1=iél.b3l b. 20% of the assembly operations will take more than how many minutes to complete? 25 as X4, 60 XalEFQ 9. Consider an infinite population with a mean of 160 and a standard deviation of 25. A random sample of size 64 is taken from this population. The standard deviation of the sample mean equals: a. 12.649 . . 9‘3 .. “ ‘5. 3.552 a’ 3: m— u 5.95 @3125 X V71 Vb‘l 10. Why is the Central Limit Theorem so important to the study of sampling distributions? a. It allows us to disregard the size of the sample selected when the population is not normal b. It allows us to disregard the shape of the sampling distribution when the size of the population is too large . It allows us to disregard the size of the population we are sampling from It allows us to disregard the shape of the population when the sample size n is large 1 1. Suppose that the amount of time teenagers spend on the intemet is normally distributed with a standard deviation of 1.5 hours. A sample of 100 teenagers is selected at random, and the sample mean computed as 6.5 hours. Determine the 95% confidence interval estimate of the population mean. 0 mm: 511 L; Gil-‘3 $1.05 0’ W"( 1131019 “7:31.195 z 4 /, w , _\ :1 . 019 , 4% W5 inmimlfl L.» m (a; ,w 3 12. A statistician wants to estimate the mean weekly family expenditure on clothes. He believes that the standard deviation of the weekly expenditure is $125. Determine with 99% confidence the number of families that must be sampled to estimate the mean weekly family expenditure on clothes to within $15. q: 135 d 1 0161‘?on fl: : 41,0.le xflfl ...
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Stats 309 ICA 2 - MTHSC 309 ICA#2 Name(s Sect 1 The...

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