Question

For each problem below, state the distribution, list the parameter values and then solve the problem. You may use Excel to solve but you still need to list the distribution name and parameter value(s). For example: Poisson distribution, x=5, p=0.24, P(5; 0.24) = 0.78 a) A skeet shooter hits a target with probability 0.6. What is the probability that they will hit at least four of the next five targets? b) You draw a random sample of 12 first graders to participate in a survey, from a class of 35 which has 16 boys and 19 girls. What is the probability that seven of the students selected will be boys? c) You are given an unlimited number of chances to complete a very difficult problem, but your grade will be lowered each chance you take. Past history says that you have a 20% chance of getting it right. What is the probability that you will get it right on the third try? Use the following for parts d through g: Cars in West Philadelphia are sold at a rate of 1.02 per day and on average 13.3% of the cars sold are considered "old" - that is they are model year 2008 or older. It seems to you - a car dealer - that the number of cars and the number of buyers and sellers in the market are very large this month compared to other moths. You decide that age of cars, number of sales and time until next sale are independent across time periods. d) Find the probability that exactly 1 of the next 7 cars sold will be an "old" car. e) Find the probability that exactly 8 cars will be sold in the next 7 days.

Answer 1

Part A)

Hitting objective whenever is free of hitting on some other time. also, the Probability of hitting effectively is consistent equivalent to 0.6. So we can utilize Binomial dispersion with n=5, p=0.6

At that point, we need to discover the likelihood that in any event 4 hits is given by

Pr(X > 4) = B(4,5,0.6)+B(5,5,0.6) = 0.2592 +0.07776 = 0.33696

Part B)

Probability of boy is 16 / 35

Binomial distribution with n=12, x=7, then resultant p = 16/35

Probability =

16 в (7, 12, 35 0.155781734

Part C)

Geometric distribution with p=0.2, x=3

Probability =

Geo(3,0.2) = 0.128

Part D)

As the two occasions are free and it's given that 7 vehicles are sold so utilizing binomial dispersion with n=7, p=0.133, Poisson Distribution

X= 1.02

Probability =

B(1,7, 0.133) 0.39542513

Part E)

For the 7 days, the period rate is 7.14

Poisson distribution with rate 7.14 and x=8

Probability =

P8, 7.14) = 0.132801374