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, ?=0.24, P(5; 0.24) = 0.78

a) A skeet shooter hits a target with probability 0.5. What is the probability that they will hit at least four of the next five targets?

b) You draw a random sample of 15 first graders to participate in a survey, from a class of 39 which has 19 boys and 20 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 30% chance of getting it right. What is the probability that you will get it right on the third try?

Use the following to solve parts d through g

Cars in Miami are sold at a rate of 1.13 per day and on average 12.3% of the cars sold are considered “old” – that is they are model year 2007 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 9 cars will be sold in the next 7 days.

f) What is the probability that it will be at least 8 days before the next car is sold?

g) Suppose no cars are sold in March. What is the probability that no cars will be sold in the first 7 days of April?

Answer 1

a) A skeet shooter hits a target with probability 0.5. What is the probability that they will hit at least four of the next five targets?

Here n = 5 is fix and the trials are independent . Also probability of success is p = 0.5 .

So the model is binomial with parameters n = 5, andd p = 0.5

We want tp find P( X >= 4) = P(X = 4) + P(X = 5)

P(X = 4) = "=BINOMDIST(4,5,0.5,0)" = 0.1563

and P(X = 5) =   "=BINOMDIST(5,5,0.5,0)" = 0.0313

P( X >= 4) = 0.1563 + 0.0313 = 0.1875

b) You draw a random sample of 15 first graders to participate in a survey, from a class of 39 which has 19 boys and 20 girls. What is the probability that seven of the students selected will be boys?

Hypergeometric distribution with parameters n = 15, a = 19, b= 20

Total ways = select 15 out of 39 = ³⁹C₁₅ = 25140840660

Possible ways = select 7 out of 19 and 8 out of 20 = 50388*125970 = 6347376360

Therefore required probability =6347376360/ 25140840660 = 0.25247272

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 30% chance of getting it right. What is the probability that you will get it right on the third try?

Geometric distribution with parameter p = 0.3

We want to find the probability that we will get it right on the third try.

That is the probability of first two try are failure and the 3rd try is success = ( 1 - 0.3 )*(1 - 0.3) *0.3 =0.147