Lefthander-acount fur about 12% of the general population. (a) In a random sampl
ID: 2922922 • Letter: L
Question
Lefthander-acount fur about 12% of the general population. (a) In a random sample of 20 people, what is the probability the there will be exnctly 3 let handers? b) What in the probability that exnetly 20 people need to be randomly selected to observe exactly 3 left handers? There are 50 women and 10 men on a bus trip. Five people are randomly selected to receive door prin. t, the random variable X be the number of men who recite nprim. ) What is the probability mass function for X? What is the probability that at least one man receives a prize? Which is more likely: 5 heads in 10 tosses of a coin; or exactly 10 heads in 20 toesee? Or are they equally likely? Assume P(heads)-.5. Explain your answer carefully 3,Explanation / Answer
Q.5 the given distribution is a binomial distribution
where probability of success = Pr(Left handed people) = 0.12
(a) sample size n = 20
Pr( X = 3; 20 ; 0.12) = 20C3 (0.12)3 (0.88)17 = 0.2242
(b) Pr(n =20 l X =3) = that means in initially 19 people, we found 2 left handed people and then the 20th one is the left handed.
Pr(n =20 l X =3) = 19C2 (0.12)3 (0.88)17 = 0.03363
Q.5
50 women and 10 men on bus trip. 5 are selected.
(a) X = number of men who receive the prizes
f(X) = 5CX10CX50C5-X/ 60C5
(a) Pr(at least one man receive the price) = 1 - Pr(no man receive the prize)
= 1 - 10C0 * 50C5/ 60C5
= 1 - 0.3879
= 0.6121
Q.6 (A) 5 heads in 10 tosses
Pr( 5 heads) = 10C5 (0.5)10 = 0.2461
Pr(10 heads out of 20) = 20C10 (0.5)20 = 0.1762
so 5 heads out of 10 is more likely than exactly 10 heads outof 20.
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