THANK YOU A study by the Center for Financial Services Innovation showed that on
ID: 2708897 • Letter: T
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THANK YOU
A study by the Center for Financial Services Innovation showed that only 64% of U.S. income earners aged 15 and older had bank accounts. If a random sample of 20 U.S. income earners aged 15 and older is selected, what is the probability that all 20 have bank accounts? no more than 15 have bank accounts? more than 10 have bank accounts? What assumptions did you have to make to answer part a? A goal keeper has a 0.89 chance per shot of preventing a goal. What is the probability that, out of ten shots taken, exactly one goal occurs? For a recent period of 100 years, the average number per year of major earthquakes (at least 6.0 on the Richter scale) was 0.93. Find the probability that no earthquakes occur in a year. What assumptions did you have to make to answer part a. Ali's water melons have a normal distribution for their diameter with mean 25.4 cm and standard deviation of 7.4 cm. What is the probability that a randomly chosen water melon has a diameter larger than 28 cm? Supermarkets reject any water melon with diameter smaller than 18cm. If you buy one of Ali's water melons from a supermarket, what is the probability that its diameter is larger than 28?Explanation / Answer
(5a)Given X~Binomial(n=20, p=0.64)
P(X=x)=xC20*(0.64^x)*((1-0.64)^(20-x))
So P(X=20) = 20C20*(0.64^20)*((1-0.64)^(20-20)) =0.0001329228
P(X<=15)=P(X=0)+P(X=1)+...+P(X=15) =0.8989375
P(X>10)= P(X=11)+..+P(X=20)=0.8576011
(b) we need to assume that X is a random variable and only have two outcomes.
(6) Given X~Binomial(n=10, p= 0.11)
P(X=x)=xC10*( 0.11^x)*((1- 0.11)^(10-x))
P(exactly one goal occurs) = 1C10*( 0.11^1)*((1- 0.11)^(10-1)) = 0.385392
(7a) Given X~Poisson(mean=0.93)
P(X=x)=(0.93^x)*exp(-0.93)/x!
P(X=0) =(0.93^0)*exp(-0.93)/1 =0.3945537
(b) We need to assume that the random variable follows poisson distriubtion.
(8a) P(X>28) = P((X-mean)/s >(28-25.4)/7.4) = P(Z>0.35) =0.3632 (from standard normal table)
(b) P(X>28) = P((X-mean)/s >(28-25.4)/7.4) = P(Z>0.35) =0.3632
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