Week6-2up - For Monday Pages 210–211 215–226 4.95 4.97...

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Unformatted text preview: For Monday: Pages 210–211, 215–226 4.95, 4.97, 4.99, 4.101 Exercises 4.37, 4.38, 4.45, 4.47, 4.49-52, 4.93, For tomorrow: Today : Pages 185 – 189 Assignments 2. Each trial results in one of two possible outcomes, identical trials in experiment. . 3. Prob. of or stays same from trial to trial. is the number of 6. Binomial Distribution 5. 4. Trials are independent.  change in the basement. 1. ¢ ¤§ Thought: People who live in glass houses should ¡ Binomial Experiment p. 179 STA 2023 c B.Presnell & D.Wackerly - Lecture 10 ¤ ¨ ¥ £ ¢ ¥ ¦§  ¡  121 ¢¨  ¥ STA 2023 c B.Presnell & D.Wackerly - Lecture 10 for ’s in the ©   trials.   ¥  !  ¢ ¤ ©  ¤ ¥ !!  ¡ ¦§ £¨ ¡ 122 to “successes”: positions terms ¤ ¤ to  terms “ ’s” : . “successes” is the product of – Think of selecting “successes”? filled with an ways to do this, so there are sample points with exactly – There are ’s. of the “ ’s” , and then filling in the rest with  £  positions to be How many sample points with exactly and  ¥  £ the probability of any sample point corresponding . The probability of this sample point is positions ¤ ¢  123 . One sample point corresponding ¤ Suppose ©  £   ¤  © ¡ ¤ §¨  ¤ STA 2023 c B.Presnell & D.Wackerly - Lecture 10  ¡ £ ¢ ¥ ¡ ¤ §¨ ¤¥¢ ¤ ¢ ¢ © £ ¦ ¢ ¦ £  ¥  ¤ ¢ ¢  ¤ £ © £ © £ §¨ ¤  ¦ £ ¤ §¨ ¢ “successes”. So, STA 2023 c B.Presnell & D.Wackerly - Lecture 10 # with errors (i) exactly 2 sheets contain errors. Find the probability that: contain errors. 5 randomly chosen sheets examined. Ex. Accountant believes 10% of all ledger sheets  © ¤§ ¥ ¡ ¥ ¤§ ¦ ©  ¥ ¤  ¥ ¥ ¥  £   !§ !§  © ¨ ¡¨ ¤ ¥  !  §¨ !§ £  ¨  ¥  ¡ ¤ ©  ¢ ¥  ¡ ¨   ¡ ¨ ¥  ¥ ¥ ¤ ¤ £ § ¥  © ¥  ¡ ¨ £  124 ¥ ¢ ¡ ¢ ¤§ ¡ ¡ ¡ ¡¨ ¢  ¢ ¦§ ¡ ¥  ¦§  ¦§  ¦ ¦ ¡¨ ¡¨ ¥ ¤§ ¤  ¥ ¥  ¥  ¡  ¢¨ (iii) more than 2 contain errors. and ¤§    £¨ ¥ ¡ Note: The following require no calculation: ¢ £ ¥ ¡  ¡ ! ¡ ¡ §  ¥ !¥ !§ (ii) at most 2 contain errors. ¡ ! ¤  ¡  ! §¨ ! §¨  ¡ ¢  ¨ !  §¨ ¡   ¨ !¥ ¨   !§  ! §¨  ¢ more work (iv) at least one contains errors. STA 2023 c B.Presnell & D.Wackerly - Lecture 10 (v) more than 1 but no more than 3 contain errors. so, ¤§  ¡ 125 ¦ § £ ¡ ¦§  ¡¨ !¥  ¨ £  ¥ ¡ ¨ ¨   ¡   ¤§ from (i), and STA 2023 c B.Presnell & D.Wackerly - Lecture 10 !  §  ! §¨ ¥ ¥ ¥ ¥ ¢¨ ¥  § ¨ ¥ ¦ § ¥ ¢¨  ¨  ¢¨ ¥ 126 =#defective is discrete is discrete Choose 2 Choose 2 =#defective 300 defective 3 defective TREAT AS BINOMIAL # who think statistics is an interesting subject students). Can treat Ex. Sample of 20 students at UF (more than 37,000 NOT BINOMIAL you expect? If I toss a balanced coin 10 times, how many heads do as a binomial random variable. ¡ 700 good bin and , sometimes , then (p. 185) defectives. Is ? switches, 128 Here . If What is the variance? . . What is the expected number of defective switches? If it is: found switches are defective. Sample of Ex. #4.51, p. 192 Supplier claims no more than 7 good abbreviated ¥ ¥ ¥ ¥ 1000 items is binomial with parameters £ 10 items If ¡ # defective in sample. ¡ ¢ ¢ ¥ ¥ ¡ £ ©¤ ©¤ Ex. Select sample of items from a shipment, and count STA 2023 c B.Presnell & D.Wackerly - Lecture 10 £   ¥ £ ¥ ¡ ¦ § ¥ ¨ ¥ ¥ ¥ !  ¢ ¤¡ £ £ 127  ¥  STA 2023 c B.Presnell & D.Wackerly - Lecture 10 ¢   § ¡ ¤ !¥  ¡ ¤ !¥ ¡   !¥ ¥ ¢   ¤¡ ¥ ¤¨ ¤ ¥ ¢ ¥  ¤ ¡ ©¤ ¥ £ ¡ !    ©¤  !¥£ £ ¡ ¢  £ ¤ score indicates that ! ¦§  ¨ ¦§  0 1 2 ¥ ¥ ¤ ¨ be obtained from these. 3 ¦ for . Any needed prob. can ..... k k+1 ..... n-1 n 1.000 1.000 5 6 9 8 1.000 1.000 1.000 1.000 4 7 1.000 3 1.000 2 ¤ ¥ gives cumulative binomial probabilities, i.e., it gives § ¥ .996 ¥  ¤§ ¡ ¤  ¨§ ¨  ¨§  ¡ ¤ ¥  1 ¡ !  The table of the binomial distribution (pp. 770–773) ¤§ !! 0 ¤ ¤ ¨ ¥ ¡ .904 k is a “rare event”. – Reject the claim– ¥ ¡  – z-score for 4 is n=10 ... ... ... ... ... ... ... ... ... ... ... .994 .954 .833 .618 .367 .166 .055 .012 .002 .000 0.60 p .972 .851 .617 .350 .150 .047 .011 .002 .000 .000 0.70 A Portion of Table II (p. 771) STA 2023 c B.Presnell & D.Wackerly - Lecture 10 0.01 § is correct?  £ if the claim  Is it likely that you would observe  ¢ 129 £ STA 2023 c B.Presnell & D.Wackerly - Lecture 10 § ... ... ... ... ... ... ... ... ... ... ... .096 .004 .000 .000 .000 .000 .000 .000 .000 .000 0.99 130 . 1 § 0 1 2 3 4 _ X<7 _ X<6 2 4 _ X<7 3 5 5 6 7 8 to find: 9 _ X>8 10 6 8 9 10 [from Table II] X=7 7 [from Table II, p. 913] 131 ¨ ¥ 0 1 3 _ X<4 2 4 5 _ X<8 7 __ 5<X<8 6 8 9 Lutheran, everyone else) ( gun owner who favors gun control, favor gun control. Interested in the number who are gun owners and ( any other (or no) rel. affil.) Interested in the number who are Lutherans 10 “more than 4 and no more than 8.” Ex. Conduct a survey, randomly select 10 indiv.: (c) ¨ STA 2023 c B.Presnell & D.Wackerly - Lecture 10 ¦§ (b) 0 : ¦§  ¨ ¥ bin ¥ (a)  ¥ § !  ¨ ¥ Ex. Use the table for ¥ STA 2023 c B.Presnell & D.Wackerly - Lecture 10 ¨ ¨   ¦§  ¤§ ¨  ¨ ¦§ §    ¥ ¦§  ¨ ¥ ¥ ¨ ¥ ¦§ ¢  ¥ ¥ £ ¦§ £ ¥ ¢ ¥ ¢ ¨ ¥ ¥ ¥ £ ¥  ¥ ¨  ¦§ ¥  ¨  ¥ £ ¥ 132 ...
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