4:46 AM Sat Mar 12 'v? 37% E]. E myopenmathcom . Question 10 v I3 0/1 pt '0 3 ('3 99 0 Details 4.3 Binomial Coefficient The first part of the binomial probability formula consists of a fraction called the binomial coefficent. It uses the factorial notation with 3 values: 1.) Number of trials n 2.) Number of successes k 3.) Number of failures (n k) n! (k!)(n k)! The binomial coefficient formula is Notice the number of trials is in the numerator and the successes/ failures are in the denominator. Example: Calculate 10 choose 4. This translates as 10 trials with 4 successes. That means the number of failures is equal to 6 since the total = successes + failures. Also (71 k) : (10 4) = 6. The binomial coefficient is 101 10-9-8-7-6-5-4-3-2-1 (4!)(6!) (4-3-2-1)(6-5-4-3-2-1) 10-9-8-7 _ 5040 _ (4-3-2-1) 24 (To make the calculations easier, try to cancel as many values as possible) Calculate 15 choose 11 This means 15 trials with 11 successess C] Question Help: 8 Message instructor Submit Question q) 4246 AM Sat Mar 12 37% E} E myopenmathcom Messages Forums Calendar Gradebook Home > STT 2640 Online SPRING 2022 D TERM > Assessment TaSk 2: Homework 2B Progress saved Done & {6' Score: 3/23 3/23 answered 0 Question 13 v [30/1 pt '0 3 Z 99 G Details 4.3 Binomial Distribution A poll is given, showing 25% are in favor of a new building project. If 7 people are chosen at random, what is the probability that exactly 6 of them favor the new building project? Round to 3 decimal places :1 Question Help: IQ Read EMessage instructor Submit Question 4:46 AM Sat Mar 12 q) 37% E]. E myopenmathcom Messages Forums Calendar Gradebook Home > STT 2640 Online SPRING 2022 D TERM > Assessment Task 2: Homework ZB Score: 3/23 3/23 answered Progress saved Done (E) 45' 0 Question 11 v 80/1 pt '0 3 :3 99 0 Details 4.3 Binomial Distribution In a Binomial Distribution with a success rate of 32.5%, find the a.) Probability of Success on a single trial p = [:] b.) Probability of Failure on a single trial q = [:] Question Help: 8 Message instructor Submit Question 4:46 AM Sat Mar 12 37% myopenmath.com Score: 3723 3723 answered Question 9 0/1 pt 9 3 99 0 Details 4.3 Factorial Notation A factorial notation is an exclamation point after a whole number. The value is found by multiplying all whole positive numbers less than or equal to the number preceding the exclamation point. For example: 9! = 9 . 8 . 7 . 6 . 5 . 4 . 3 . 2 . 1 = 362, 880 Note: In the special case 0! = 1 Find the values of the following factorial values a. ) 4! = b. ) 5! = C. ) 6! = Question Help: Message instructor Submit Question4:46 AM Sat Mar 12 37% myopenmath.com Home > STT 2640 Online SPRING 2022 D TERM > Assessment Task 2: Homework 2B Progress saved Done Score: 3/23 3/23 answered Question 12 0/1 pt 9 3 99 0 Details 4.3 Binomial Distribution Using the Binomial distribution, If n = 5 and p = 0.3, find P(X = 4) This translates to 4 successes and 1 failure(s) in 5 trials Round to 3 decimal places. Binomial Formula n! P( X = k) = - k ! . ( n - k ) ! . ph . qn - k Question Help: Read Message instructor Submit Questionq) 4246 AM Sat Mar 12 37% E} E myopenmathcom Messages Forums Calendar Gradebook Home > STT 2640 Online SPRING 2022 D TERM > Assessment TaSk 2: Homework 2B Progress saved Done & {6' Score: 3/23 3/23 answered 0 Question 14 v [30/1 pt '0 3 Z 99 G Details 4.3 Binomial Distribution A manufacturing machine has a 5% defect rate. If 4 items are chosen at random, what is the probability that at least one will have a defect? Round to 3 decimal places Question Help: I2 Read EMessage instructor Submit