Question

Question 1:

Suppose you draw a sample of four skittles (with replacement) from a large jar containing 5,333 skittles. You record whether each of the four skittles is ORANGE or NOT ORANGE on each draw.  There are 955 orange skittles in the jar.

What is the probability of drawing an orange skittle from the jar? Round to two decimal places.

Question 2:

Suppose you draw a sample of four skittles (with replacement) from a large jar containing 5,333 skittles. You record whether each of the four skittles is ORANGE or NOT ORANGE on each draw.  There are 955 orange skittles in the jar.

Using your answer from Question #1, what is the probability of drawing no orange skittles in four draws? Round to two decimal places.

Question 3:

Suppose you draw a sample of four skittles (with replacement) from a large jar containing 5,333 skittles. You record whether each of the four skittles is ORANGE or NOT ORANGE on each draw.  There are 955 orange skittles in the jar.

Using your answer from Question #1 and #2, what is the probability of drawing no more than 1 orange skittle in four draws? Round to two decimal places.

Question 4:

Suppose you draw a sample of four skittles (with replacement) from a large jar containing 5,333 skittles. You record whether each of the four skittles is ORANGE or NOT ORANGE on each draw.  There are 955 orange skittles in the jar.

Use your answer from Question #1 to calculate the expected number of orange skittles in four draws. Round to two decimal places.

Question 5:

Suppose you draw a sample of four skittles (with replacement) from a large jar containing 5,333 skittles.  You record whether each of the four skittles is ORANGE or NOT ORANGE on each draw.  There are 955 orange skittles in the jar.  

Use your answer from Question #1 to calculate the standard deviation for the number of orange skittles in four draws. Round to two decimal places.

Answer 1

1)

Given

Total number of observations (n)= number of skittles in a sample = 4

p = probability of success = probability of drawing an orange skittle = 955 / 5333 = 0.179

Let x be the number of drawing orange skittle.

Now, by Binomial probability,

  

Therefore,the probability of drawing an orange skittle from the jar = 0.40

2)

Given

X= 0

Now

  

Therefore, the probability of drawing no orange skittles in four draws = 0.45

3)

  

  

Therefore, the probability of drawing no more than 1 orange skittle in four draws = 0.85

4)

Since X follows binomial distribution,

the mean ( expected value ) of the binomial distribution is given by

Therefore, the expected number of orange skittles in four draws = 0.72

5)

The standard deviation of the binomial distribution is given by

So,

Therefore, the standard deviation for the number of orange skittles in four draws = 0.77