question 1

Suppose that the random variable x, shown below, represents the number of speeding tickets a person received in a three-year period. P(x) represents the probability of a randomly selected person having received that number of speeding tickets during that period. Use the probability distribution table shown below to answer the following questions.

x	P(x)
0	0.3322
1	0.285
2	0.1825
3	0.1237
4	0.0452
5	0.0314
6+	0.0000

a) What is the probability that a randomly selected person has received four tickets in a three-year period? P(x =4)= b) What is the probability that a randomly selected person has received four or more tickets in a three-year period? P(x= 4)= c) What is the probability that a randomly selected person has received more than four tickets in a three-year period? P (x > 4 )= d) Would it be unusual to randomly select a person who has received four tickets in a three-year period?

• Yes
• No

question 2

It is estimated that 40% of Kickstarter projects are successfully funded. Assume each Kickstarter project is independent. A random sample of 18 Kickstarter projects are followed. Let be the number Kickstarter projects that are successfully funded. Calculate the following:

a. u X:

b. o X:

c. P(X=8):

d. P(X <9 ):

e. P (X> 5):

f. (X 5):

g. P(5 X 9):

question 3

When dragons on planet Dathomir lay eggs, the eggs are either green or yellow. The biologists have observed over the years that 21% of the eggs are yellow, and the rest green. Next spring, the lead scientist has permission to randomly select 61 of the dragon eggs to incubate. Consider all the possible samples of 61 dragon eggs. What is the mean (u) number of yellow eggs in samples of 61 eggs? u = (Please show your answer to 1 decimal place) What is the standard deviation (u) in the number of yellow eggs in samples of size 61? q = (Please show your answer to 1 decimal place)

question 4

A variable x is normally distributed with mean 19 and standard deviation 8. Round your answers to the nearest hundredth as needed. a) Determine the z-score for x=23.

b) Determine the z-score for x=14.

c) What value of x has a z-score of 1.38?

d) What value of x has a z-score of -0.5?

e) What value of x has a z-score of 0?

Question 5

Suppose that a box contains 7 cameras and that 5 of them are defective. A sample of 2 cameras is selected at random. Define the random variable xas the number of defective cameras in the sample. Write the probability distribution for x

x	P(x)

What is the expected value of x?

question 6

x	P(x)
0	0.25
1	0.1
2	0.1
3	0.55

Find the standard deviation of this probability distribution. Give your answer to at least 2 decimal places

question 7

x	P(x)
0	0.25
1	0.05
2	0.3
3	0.4

Find the mean of this probability distribution. Round your answer to one decimal place.

Question 8

Construct a probability distribution for the given frequency distribution.

(Hint: There were 160 individuals in this sample.)

x	Frequency
200	4
250	5
300	2
350	16
400	6
450	46
500	34
550	6
600	41

Probability Distribution:

x	P(x)
200
250
300
350
400
450
500
550
600

question 9

Recall that a normal distribution is, bell-shaped, symmetric, where the mean, median and mode are the same. Simply put, it is a data set where most values are around the mean.

Come up with a real-life data set that is normally distributed. Write at least two sentences on why your data set exhibits the characteristics of the normal distribution.

Come up with your own example! There are many examples of naturally-occurring data sets that are normally distributed.]

Please, answer the questions sequentially. Thanks.