Question

(b) Randomly draw a card from a standard deck of playing cards (32 cards), let Bvent B be: "the card is & Diamond Face card" (note: "Face card means, P(B) (4b) Note: The folowing table deecribes the smokdng habita of a group of asthma suffers Answer (c) and (d) according to the table. | Nonsmoker Occasional smoker Regular smoker Heay smokerotal) Women 377 32 84 28 521 148 65 (e) Event C is "a randomly selected person in the group is a P(C) femae (4c) (d) Event D is "a randomly selected person in the group is a male and a smoker. P(D)-? (4d) find P(-0.38 < z < 1.25) z is standard normal random variable. (e) (f) z is standard normal random variable. if P(z> a) 0.875, a (4f) (g) z is a normal random variable, z~N(45,5), find P(z> 41) (4g)

Answer 1

(b) required probability=P(B)=3/52 ( since there are 3 diamond face card out of 52 cards)

(c)P(C)=521/991

(d)P(male and smoker)=(33+64+34)/991=131/991

(e)P(-0.38<Z<1.25)=P(Z<1.25)-P(Z<-0.38)=0.8944-0.3520=0.5424

(f) P(Z>a)=0.875

or, 1-P(Z<a)=0.875

or, P(Z<a)=0.125

or a=-1.15

(g) here we use standard normal variate z=(x-mean)/sd

for x=41, z=(41-45)/sqrt(5)=-1.7888

P(X>41)=P(Z>-1.7888)=1-P(Z<-1.7888)=1-0.0368=0.9632