Free Response 19.) Decide whether the situation described is a binomial setting, a geometric setting or neither. a. Suppose you repeatedly draw cards out of a deck without replacement in an attempt to draw an ace. neither b.) You roll a die 20 times and count the number of 1's you rolled. 20 Biganial() c.) You attempt to find a parking space at the mall on Christmas eve, so you drive up the parking lot aisle until you find an empty parking space. probability of succeir choyer Neither-fry the Farther you from the d.) In an advertisement, you see that 24% of Americans use Crest toothpaste. So you take a random sample of 50 Americans and count the number who uses Crest toothpaste Biemal e.) You flip a coin until you get a tails. Geometric 1.) 8% of the apples at the supermarket have a bruise on it. You randomly choose apples from the fruit bin at Stew Leonard's until you find one with a bruise. Geometric g.) You randomly choose 20 apples from the fruit bin and count the number of apples without a bruise. Binomial 20.) 63% of the freshmen who enroll at Penn State University will graduate in 4 years. Suppose you are a freshman at Penn State and there are 16 freshmen who live on your dorm floor. a.) What is the probability that exactly half of the freshman on your floor will graduate in 4 years? Bomal P(x=8)→ 7=16 2.63 61122 binampdf (16,63,8) b.) What is the probability that more than 10 freshmen on your floor will graduate in 4 years? 7=1692.63 P(X10) = 1-P(X≤10)=1-binam (16.63,10)=(-4230 c.) How many freshmen on your floor would you expect to graduate in 4 years? Binamal E(x)=np=16(163)=10.08 d.) What is the standard deviation of this distribution? 50(x)=√Apq = √(63) (37) = (1.93 e.) What is the probability that the mean? number of freshmen who graduate will be within 1 standard deviation of the (8.15 2) = 1 - f(x <= 2) 1- Geomatedf (183,2)=(10289 e.] On average, how many rolls will it take Norm until he rolls his first strike? 6arutameye= 1/p = 1/13 = boxed 1.205 22.) in order to interview Iraqi terrorists, the FBI needs agents that speak the Iraqi language. It is known that 4% of FBI agents are fluent in the Iraqi language. So the director of the FBI goes thorough a list of agents. a.) On average, how many agents will the head of the FBI have to go through until he finds an agent who is 1x250m² E(x)= 1P = 1/0.04 = boxed 25 fluent in the Iraqi language? b.] What is the probability that the 11th person on the list is the first agent to be fluent in the Iraqi language? varphi = 0.04 k = 11 Geanut pdf (109,11)=0266 c.) What is the probability that the director will have to go through more than 20 names before he finds his first agent who is fluent in the Iraqi language? f(x > 20) = 1 - p(x <= 20) 1-Geametedf (.04, 20).4420 23.) A wildlife biologist examines frogs for a genetic trait he suspects may be linked to sensitivity to industrial toxins in the environment. Previous research had established that this trait is usually found in 1 of every 8 frogs. He collects and examines a dozen frogs. If the frequency of the trait has not changed, what's the probability he finds the trait in a) none of the 12 frogs? bnomal rho = 1/8 f = 12 P(A=0) bine (12,1,0)=2014 b.) at least 2 frogs? P(x22)=1-P(x-1)=1-bnanedf (12,½, 1) = 4533 c.) 3 or 4 frogs? P(x=3) or P(X=4) = binampdf (12,1,3) + bompdf (12, 4) = (-1707 d.) no more than 4 frogs? P(xs 4) = brancadf (12, 1, 1) = (09887

Sats Unit 5 Review

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