Reference no: EM13954344
1. 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) _____________________
b). What is the probability Joe will make a profit in the first six months? ________________________________
2. 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:
3. 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.
___ _______________
4. 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) (1 pt ea)
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:
_______________________________________________________
5. 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 =
6. 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:
7. Suppose 10-mile race times have an average runnerâ??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?
_______________________