1. Richwood Products buys parts from Staple Brothers machining. The engineers at Richwood want to ensure that the parts purchased meet their company's standards. Their engineers take a random sample of 5000 parts from all of the parts purchased from Staple and test to see if the parts are defective. Out of the 5000 parts, 75 were found to be unacceptable - yielding a defect rate of 1.5%. The engineers reported back that less than 2% of all parts purchased from Staple Brothers are defective.
a). Population
b). Sample
c). Variable
d). Type of measurement scale
e). A piece of datum
f). Statistic
g). Parameter
2. For the sample data set: {8, 17, 10, 25, 10, 14}
Identify:
a). Mean:
b). Median:
c). Mode:
d). 70th Percentile:
e). 1st Quartile
f). 3rd Quartile :
g). Variance
h). Standard deviation:
3. Fill in the blank with the appropriate values given the following frequency distribution of a sample of data:
|
Value, x
|
Frequency, f
|
x * f
|
( x -  )2 * f
|
|
20
|
5
|
|
|
|
21
|
7
|
|
|
|
22
|
1
|
|
|
|
23
|
3
|
|
|
|
TOTAL
|
|
|
|
Find:
a). The sample weighted mean:
b). The median:
c). The sample standard deviation:
d). The 85th percentile:
4. Given the following values, create a scale and a boxplot. Give the numerical values of the 5-number summary on the boxplot. Show the values that would be used to determine the outliers, and graph and label any in the data. Also, compute the interquartile range (IQR).
|
21
|
12
|
31
|
89
|
64
|
31
|
75
|
42
|
50
|
64
|
80
|
43
|
a). Boxplot: (Five number summary _____, ______, _____, _____, _____)
b). The IQR is:
c). Give the values that would be used to determine if there are outliers.
_________________________________
d). If there are outliers, what are they?
5. The distribution of weights of parts produced during the month of November is normally distributed with a mean weight of 200 grams and a standard deviation of 10 grams.
a) What is the z-score for a weight of 210? _____________
b) What weight would we expect 50% of the packages to weigh more than? ____
What percent of the packages:
c). Weigh between 170 and 230 grams?
d). Weigh less than 190 grams?
6. Write the correct letter next to the symbols below. The following paragraph gives all of the required information:
A simple random sample of 60 one-gallon pails was taken from a batch of 3000 one-gallon pails of ice cream. The sample had a mean weight of 123.8 ounces with a standard deviation of 2.4 ounces. All of the 3000 pails had a mean weight of 127.2 ounces with a standard deviation of 1.4 ounces.
Give letter of the value that is represented by each symbol:
|
_____
|
µ
|
a.
|
60
|
|
_____
|
s
|
b.
|
3000
|
|
_____
|
n
|
c.
|
123.8
|
|
_____
|
s
|
d.
|
127.2
|
|
_____
|
|
e.
|
1.4
|
|
_____
|
N
|
f.
|
2.4
|
|
|
|
|
|
7. Given the following data:
a). Compute the relative frequency and the cumulative frequency distribution table for the data.
|
Price range
|
Frequency
|
Relative
Frequency
|
Cumulative
Frequency
|
|
31 - 35
|
5
|
|
|
|
36 - 40
|
10
|
|
|
|
41 - 45
|
17
|
|
|
|
46 - 50
|
8
|
|
|
b). Sketch the frequency histogram for the data.
8. Joe is considering one of three locations for his business. There is a 45% probability he will choose location A, a 25% probability he will choose B and a 30% probability he will choose location C. If he chooses A the probability that he will make a profit in the first six months is 55%, if he chooses B the probability of making a profit in the first six months is 50% and if he chooses C the probability of making a profit in the first six months is 35%.
Determine the following probabilities to three decimal places.
a). What is the probability that Joe will choose location A and make a profit in the first six months? P(Location A and makes a profit)
______ _____________
b) What is the probability that Joe will choose location C and does NOT make a profit in the first six months? P(Location C and does not make a profit)
_____________________
c). What is the probability Joe will make a profit in the first six months?________________________________
9. ABC home builders sold 50 new homes last year. Of the homes, 20 have skylights; 25 have attached garages; and 5 have both a skylight and an attached garage. Others have neither garages nor skylights.
Determine the following probabilities to three decimal places.
Find the probability that a randomly selected house will:
a). Have both a skylight and an attached garage:
b). Have a skylight only:
c). Have either a skylight or an attached garage (or both):
d). Have a skylight given that we know it has an attached garage:
e). Have an attached garage given that we know it has a skylight:
10. The executives at a text book publishing company wants to gather data from universities on statistics text books currently in use. Identify the correct sampling method being used in each of the following scenarios:
a.) Using a list of all universities in the United States, they randomly choose a number between 1 and 35 to be the first university questioned. Then they question every 17thth university after the first one. __ ________________
b.) They list all of the universities in the United States. Then 100 random numbers are generated and the universities that correspond with the random numbers are chosen.__ ________________
c.) They randomly select 25 states from all states in the United States and question every university in each of the 25 states. ___ _______________
d.) They randomly select 30 universities from each state in the United States and question these selected universities.
___ _______________
11. A group of 300 heads of households was surveyed to determine if their marital status was related to home ownership. Complete the table to answer the questions below:
|
|
Marital Status
|
|
|
Living
Status
|
Single (never married)
|
Divorced
|
Married
|
Totals
|
|
Own home
|
33
|
39
|
83
|
|
|
Rent
|
15
|
18
|
52
|
|
|
Live with family
|
32
|
13
|
15
|
|
|
Totals
|
|
|
|
300
|
Determine each probability: (Round answers to three decimal places)
a). What is the probability that a randomly selected head of household will rent?
b). What is the probability that a randomly selected head of household will be single?
c). What is the probability that a randomly selected head of household will own a home and be married?
d). What is the probability that a randomly selected head of household is single given he/she lives with a family?
e). What is the probability that a randomly selected head of household will rent given he/she is divorced?
f). What is the probability that a randomly selected head of household will rent given he/she is married?
g). Are marital status and living situation independent or dependent?
h). Explain your answer in part g using probabilities:
12. Given the following probability distribution, determine the given probabilities:
|
x
|
P(x)
|
|
0
|
0.10
|
|
1
|
0.20
|
|
2
|
0.55
|
|
3
|
0.15
|
a). P(x < 1) =
b). P(1 < x < 3) =
c). P(x > 2) =
d). P(1 < x < 3) =
e). Expected value of x =
f). Standard deviation =
13. A study shows that 20% of cars in the state of Ohio have improperly functioning emission control systems. If a random sample of 15 cars is taken, determine the following: (Round answers to three decimal places)
a). What type of probability distribution does this describe and why?__ ______
b). The probability that exactly 2 will be improperly functioning:
c). The probability that no more than 2 will be improperly functioning:
d). The probability that at least 2 are improperly functioning:
e). The expected number of cars with improperly functioning systems out of the sample of 15:
f). The standard deviation of the probability distribution:
14. Suppose 10-mile race times have an average runner's finish time of 80 minutes with a standard deviation of 7 minutes. There is strong reason to believe the times are NOT normally distributed.
a). If 750 people run, at least how many people will have finish times within 2 standard deviations of the mean? _______________
b). If you were one of these people, in what time interval would you have run the race? _______________________