Question

Binomial Distribution:
A college finds that 40 percent of all students take a course in statistics. Success is defined as a student not taking a course in statistics.
P(Success) = P(student does not take statistics) = 1- .4000 =.6000 .

If a group of 8 students are considered: What is the probability that less than 3 students do not take statistics? (use the table in the back of your textbook) (do not round)

Answer 1

P(Less than 3 do not take statistics)

= P(X < 3)

= P(X < 2)

= binom.dist(2, 8, 0.60, TRUE) [Excel Formula]

= 0.3154

Answer 2

A group of 8 students are considered. A college finds that 40 percent of all students take a course in statistics. Success is defined as a student not taking a course in statistics. P(Success) = P(student does not take statistics) = 1-0.40 = 0.60 Let the random variable X represents number of students do not take statistics in a sample of 8. Here, X ~ Binom(n=8, p=0.60) The PMF of X can be written as, P(X= x)= (*) p*(1-p)* 0.60)' (1-0.60) **, x=0,1,2,...,8 That is, P(x = x) = (9)(0.6)*(0,4)** .-(1) Using the above equation (I), calculate the probability that X <3. P(.x <3)=P(X 52) = P( X = 0)+P( X = 1)+P( X = 2) - 0) (0.6)*(0.4)** + (0) (0.6) (0.4)*4 +(9 (0.6) (0.4)* = 0.0007 +0.0079 +0.0413 = 0.0498

F_() = P(X=1- p-1 - p)-> 0.1 0.2 0.25 0.3 0.4 0.5 0.6 0.7 0.75 0.8 0.9 70 0.4783 0.2097 0.1335 0.0824 0.0280 0.0078 0.0016 0.0002 0.0001 0.0000 0.0000 1 0.8503 0.5767 0.4449 0.3294 0.1586 0.0625 0.0188 0.0038 0.0013 0.0004 0.0000 2 0.9743 0.8520 0.7564 0.6471 0.4199 0.2266 0.0963 0.0288 0.0129 0.0047 0.0002 3 0.9973 0.9667 0.9294 0.8740 0.7102 0.5000 0.2898 0.1260 0.0706 0.0333 0.0027 4 0.9998 0.9953 0.9871 0.9712 0.9037 0.7734 0.5801 0.3529 0.2436 0.1480 0.0257 5 1.0000 0.9996 0.9987 0.9962 0.9812 0.9375 0.8414 0.6706 0.5551 0.4233 0.1497 6 1.0000 10000 0.9999 0.9998 0.9984 0.9922 0.9720 0.9176 0.8665 0.7903 0.5217 7 1.0000 10000 10000 10000 10000 10000 1.0000 1.0000 10000 10000 10000 0.4305 0.1678 0.1001 0.0576 0.0168 0.0039 0.0007 0.0001 0.0000 0.0000 0.0000 1 0.8131 0.5033 0.3671 0.2553 0.1064 0.0352 0.0085 0.0013 0.0004 0.0001 0.0000 0.9619 0.7969 0.6785 0.5518 0.3154 0.1445 0.0498 0.0113 0.0042 0.0012 0.0000 3 0.9950 0.9437 0.8862 0.8059 0.5941 0.3633 0.1737 0.0580 0.0273 0.0104 0.0004 4 0.9996 0.9896 0.9727 0.9420 0.8263 0.6367 0.4059 0.1941 0.1138 0.0563 0.0050 5 1.0000 0.9988 0.9958 0.9887 0.9502 0.8555 0.6846 0.4482 0.3215 0.2031 0.0381 6 1,0000 0.9999 0.9996 0.9987 0.9915 0.9648 0.8936 0.7447 0.6329 0.4967 0.1869 7 1.0000 10000 1.0000 0.9999 0.9993 0.9961 0.9832 0.9424 0.8999 0.8322 0.5695 8 1.0000 10000 10000 10000 10000 10000 10000 10000 10000 10000 10000 From the binomial table also, P(X < 2) = 0.0498 If a group of 8 students are considered, the probability that less than 3 students do not take statistics is 0.0498.