Question

At Perry’s Pumpkin Patch there are 50 pumpkins to choose from in four different colors. Five pumpkins are yellow, 12 are green, 6 are white and the rest are orange pumpkins. Answer the following questions. PLEASE SHOW STEPS/CALCULATIONS

a) You will randomly choose 8 pumpkins to take home with you. What is the probability that you have chosen at least 2 orange pumpkins? What distribution, parameter(s), and support are you using?

b) Given that you have chosen at least 2 orange pumpkins, what is the probability that you have chosen fewer than 5 orange pumpkins?

c) What is the expected value and standard deviation of the number of white pumpkins you have chosen?

d) Over on another field there are 300 pumpkins, 20 of which are white. You are going to randomly choose 10 pumpkins from this larger field. What is the probability that you have chosen at most one white pumpkin from the second field?

e) Is there an approximation that can be used on the second field to find the probability that you have chosen at most one white pumpkin? Justify why you can or cannot use an approximation and state its distribution, parameter(s), and support.

f) Find the approximate probability that you have chosen at most one white pumpkin from the second field.

Answer 1

There are 27 orange pumpkins and 23 rest pumpkins.

a) This can be solved using the binomial distribution:

The probability that pumpkin is orange:

The total number of trials: n=8

The probability that you have to choose at least 2 orange pumpkins =

b) the probability that you have chosen fewer than 5 orange pumpkins Given that you have chosen at least 2 orange pumpkins = the probability that you have chosen fewer than 5 and at least 2 orange pumpkins / ( the probability that you have chosen at least 2 orange pumpkins)

the probability that you have chosen fewer than 5 and at least 2 orange pumpkins =

c) Number of white pumpkins can be X = 0,1,2.........,6

The probability that pumpkin is white:

The total number of trials: n=8

X	P(X)
0
1
2
3
4
5
6

Expected value=

Standard deviation =

d) probability that the pumpkin is white

total number of trials: n=10

the probability that you have chosen at most one white pumpkin from the second field =