Question 317779: Please, please and thx in adv. I have been studying for almost 4 days already for my algebra exam. I can't figure these problem out. Please help.
1) At a local college 55% of the students are female and 45% are male. Also 40% of the female students are education majors and 15% of the males are education majors.
a) what are the probability a student selected at random is male and education major?
b) what are the probability a student selected is an education major?
c) what are the probability a student is female given the person is an education major?
2) E and F are independent events. Find P(E) if P(EUF) = 0.6 and P(F)= 0.1.
3) At the college of Old Westbury, 20% of the students majors and the rest major in something else. Although 70% of the students majors take finite mathematics, only 10% of the other majors take finite mathematics. A student is chosen at random. She is taking finite mathematics. What is the probability she is a business major?
4) A lung cancer test has been found to have the following reliability. The test detects 85% of the people who have cancer and does not detect 15% of these people. Among the noncancerous group it detect 92% of the people not having cancer, whereas 89% of this group are detected erroneously as having lung cancer. Statistics show that about 1.8% of the population has ling cancer. Suppose an individual is given the test for lung cancer and it detected his disease. What is the probability that the person actually has lung cancer?
5) Shrimp are priced by size; the larger the shrimp, the more expensive the cost. Jumbo shrimp have 9 shrimp to the pound with a standard deviation of 0.75 shrimp. What is the probability that a pound of jumbo shrimp contains fewer than 8 or more than 10 shrimp?
6) Compute the Z-score for the data point X, using the given population mean and standard deviation.
µ = 32, σ = 13, x = 10
7) Calculate the area under the normal curve.
Between Z = -1.5 and Z = 0.34
8) Bob got an 89 on the final exam in mathematics and a 79 on the sociology exam. In the mathematics class, the average grade was 79 with a standard deviation of 5, and in the sociology class the average grade was 72 with a standard deviation of 3.5. Assuming that the grades in both subjects were normally distributed, in which class did Bob rank higher?
9) From past experience a teacher knows that the test scores of students taking an examination have a mean of 75 and a variance of 25. What can be said about the probability that a student will score between 65 and 85?
Please show me the steps this way I can learn them too. Thank you.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 1) At a local college 55% of the students are female and 45% are male. Also 40% of the female students are education majors and 15% of the males are education majors.
a) what are the probability a student selected at random is male and education major?
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P(m and e) = P(e|m)*P(m) = 0.15*0.45
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b) what are the probability a student selected is an education major?
P(e) = P(e and m) + P(e and f) = P(e|m)*P(m) + P(e|f)*P(f)
= 0.15*0.45 + 0.40*0.55
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c) what are the probability a student is female given the person is an education major?
P(f|e) = P(f and e)/P(e) = [0.40*0.55]/[0.15*0.45 + 0.40*0.55]
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2) E and F are independent events. Find P(E) if P(EUF) = 0.6 and P(F)= 0.1
P(E and F) = P(E)+P(F)-P(E or F)
= P(E)+0.1-0.7
= P(E)-0.6
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But E and F are independent, so
P(E and F) = P(E)*P(F) = 0.1*P(E)
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So you have two expressions for P(E and F); equate them to get:
P(E)-0.6 = 0.1*P(E)
0.9*P(E) = 0.6
P(E) = 0.6/0.9 = 2/3
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3) At the college of Old Westbury, 20% of the students majors and the rest major in something else.
Although 70% of the students majors take finite mathematics, only 10% of the other majors take finite mathematics.
A student is chosen at random. She is taking finite mathematics. What is the probability she is a business major?
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P(bm |finite math) = P(bm and fm)/[P(fm)]
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Note: Your 1st sentence is missing a word or two; probably the word
"business".
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4) A lung cancer test has been found to have the following reliability.
The test detects 85% of the people who have cancer and does not detect 15% of these people.
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Among the noncancerous group it detect 92% of the people not having cancer, whereas 8% of this group are detected erroneously as having lung cancer.
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Statistics show that about 1.8% of the population has lung cancer. Suppose an individual is given the test for lung cancer and it detected his disease. What is the probability that the person actually has lung cancer?
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P(can |+) = P(can and +)/P(+)
= [P(+|can)*P(can)]/[P(can and +) + P(can' and +)]
= [0.85*0.018]/[(0.85*0.018) + P(+|can')*P(can')]
= [0.85*0.018]/[0.85*0.18 + 0.08*0.0.982]
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5) Shrimp are priced by size; the larger the shrimp, the more expensive the cost. Jumbo shrimp have 9 shrimp to the pound with a standard deviation of 0.75 shrimp. What is the probability that a pound of jumbo shrimp contains fewer than 8 or more than 10 shrimp?
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z(8) = (8-9)/0.75 = -1/(3/4) = -4/3
z(10) = (10-9)/0.75 = 1/(3/4) = 4/3
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P(8 < x < 10) = P(-4/3 < z < 4/3) = normalcdf(-4/3,4/3) = 0.8176
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6) Compute the Z-score for the data point X, using the given population mean and standard deviation.
µ = 32, σ = 13, x = 10
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z(10) = (10-32)/13 = -1.6923
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7) Calculate the area under the normal curve.
Between Z = -1.5 and Z = 0.34
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normalcdf(-1.5,0.34) = 0.5663
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8) Bob got an 89 on the final exam in mathematics and a 79 on the sociology exam. In the mathematics class, the average grade was 79 with a standard deviation of 5, and in the sociology class the average grade was 72 with a standard deviation of 3.5. Assuming that the grades in both subjects were normally distributed, in which class did Bob rank higher?
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Math: z(89) = (89-79)/5 = 2
Socy: z(79) = (79-72)/3.5 = 2
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Ans: He ranked the same in both classes.
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9) From past experience a teacher knows that the test scores of students taking an examination have a mean of 75 and a variance of 25. What can be said about the probability that a student will score between 65 and 85?
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std = sqrt(25) = 5
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P(65 < x < 85) = P(z(65) < z < z(85)) = 0.9545
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Cheers,
Stan H.
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