6.4 approximating binomial distr with normal curve.notebook January 26, compute the mean/ expected value for the above distribution.

Transcription

1 Discrete: Countable (no fractions or decimals) Continuous: Measurable: distance, time, volume Binomial Distribution n = number of trials r = number of successes p = probability of success q = probability of failure q = 1 p Make a histogram for the binomial distribution where p =.25, q =.75 and n = 3. Find the P(r) values in the chart: or Type 0 3 into list 1 and binomialpdf(3,.25,l1) into list 2 r P(r) compute the mean/ expected value for the above distribution. 1. Can put r values into list 1 and probabilities into list 2. 1 var stat L1, L2 2. Can multiply 0(.422) + 1(.422) + 2(.141) + 3(.016) 3. Can use the formula answer:.751 answer:.752 answer:.75 compute the standard deviation for the distributions answer:.7 answer:.7

2 Watch what happens to the shape of the histogram as we increase the value of n. np =.75 nq=2.25 np = 2.5 nq= 7.5

3 np = 6.25 nq= np = 12.5 nq= 37.5

4 If np > 5 and nq > 5 then a binomial distribution can be approximated by a normal distribution. (Use the techniques you learned in chapter 6) Use the continuity correction to get a better approximation. If you are finding the area to the right If you are finding the area to the right, then subtract.5 from r. P(r > 8) will become P( x > 7.5)

5 If you are finding the area to the left If you are finding the area to the left, then add on.5 to r. so P(r < 8) will become P(x < 8.5)

6 If you are finding the area between two values If you are finding the area between two values then do both: so P(4 < r < 7) will become P(3.5 < x < 7.5)

7 Compare the two methods: If we know that p =.25 and n = 25 then find P(r > 8). Binomial n = 25 p = 0.25 P(r 8) reminders put 0 25 in L1 hover over L2 type binomialpdf (n,p,l1) answer P(r > 8 ) = = 27.25%

8 If we know that p =.25 and n = 25 then find the P(r > 8). Use the Normal/Standard Normal curve: Need reminders and changes to for better accuracy answer

9 About 40% of all US adults will try to pad their insurance claims. Suppose that you are the director of an insurance adjustment office. Your office has just received 128 insurance claims to be processed in the next few days. What is the probability that half or more of the claims have been padded? discrete or continuous? n = 128 p =.4 q = 1.4=.6 Check: n p= n q= Continuity Correction: r > 64 x > 63.5

10 About 40% of all US adults will try to pad their insurance claims. Suppose that you are the director of an insurance adjustment office. Your office has just received 128 insurance claims to be processed in the next few days. What is the probability that fewer than 45 of the claims have been padded? discrete or continuous? n = 128 p =.4 q = 1.4=.6 Check: n p= n q= Continuity Correction: r < 45 x < 45.5

11 About 40% of all US adults will try to pad their insurance claims. Suppose that you are the director of an insurance adjustment office. Your office has just received 128 insurance claims to be processed in the next few days. What is the probability that from 40 to 60 of the claims have been padded? discrete or continuous? n = 128 p =.4 q = 1.4=.6 Check: n p= n q= Continuity Correction: 40 < r < 60

12 6.4 approximating binomial distr with normal curve.notebook January 26, 2018

13 USA Today reported that 11% of all books sold are romance oriented. If a local bookstore sells 316 books on a given day, what is the probability that a) no more than 40 are romances? discrete or continuous? n = 316 p =.11 q = 1.11=.89 Check: n p= n q= Continuity Correction: r < 40 x < 40.5

14 USA Today reported that 11% of all books sold are romance oriented. If a local bookstore sells 316 books on a given day, what is the probability that a) at least 25 are romances? discrete or continuous? n = 316 p =.11 q = 1.11=.89 Check: n p= n q= Continuity Correction: r > 25 x > 24.5

15 6.4 approximating binomial distr with normal curve.notebook January 26, 2018

16 USA Today reported that 11% of all books sold are romance oriented. If a local bookstore sells 316 books on a given day, what is the probability that c) between 25 and 40 are romances? discrete or continuous? n = 316 p =.11 q = 1.11=.89 Check: n p= n q= Continuity Correction: 25 < r < < x < 40.5

17 d) in the solution to this problem what was n? p? q? Does it appear that both np and nq are larger than 5? Why is this important consideration?

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20 P. 341 #3 15 choose any 9 note: s d n