Please show steps. Thanks! 1. At a college, 70 percent of the students are women
ID: 3432612 • Letter: P
Question
Please show steps. Thanks!
1. At a college, 70 percent of the students are women and 50 percent of the students receive a grade of C. 25 percent of the students are neither female nor C students. Use this table:
C Not C
Women .45 .25
Men .05 .25
If the student is a C student, find the probability the student is a male.
2. An important part of the customer service responsibilities of a cable company relates to the speed with which trouble in service can be repaired. Historically, the data show that the likelihood is 0.80 that troubles in a residential service can be repaired on the same day. For the first eight troubles reported on a given day, what is the probability that: At least 4 troubles will be repaired on the same day.
3. The J.O. Supplies Company buys calculators from a Korean supplier. The probability of a defective calculator is 10%. If 14 calculators are selected at random, what is the probability that less than 5 of the calculators will be defective?
4. The number of items rejected daily by a manufacturer because of defects for the last 30 days are: 20, 21, 8, 17, 25, 19, 18, 19, 14, 17, 11, 6, 21, 25, 4, 19, 9, 12, 16, 16, 10, 28, 24, 6, 21, 20, 25, 5, 17, 10. Complete the following frequency table for these data:
Frequency Rel. Freq. Cumulative Rel. Freq.
4 < 9
9 < 14
14 < 19
19 < 24
24 < 29
Explanation / Answer
(1) the probability the student is a male is
P(male|C) = P(male and C)/P(C)
=0.05/(0.45+0.05)
=0.1
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(2)Given X follows Binomial distribution with n=8 and p=0.8
P(X=x)=8Cx*(0.8^x)*(0.2^(8-x)) for x=0,1,2,...,8
So the probability is
P(X>=4) = P(X=4)+P(X=5)+P(X=6)+P(X=7)+P(X=8)
=8C4*(0.8^4)*(0.2^(8-4))+...+8C8*(0.8^8)*(0.2^(8-8))
=0.9895936
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(3)Given X follows Binomial distribution with n=14 and p=0.1
P(X=x)=14Cx*(0.1^x)*(0.9^(14-x)) for x=0,1,2,..,14
So the probability is
P(X<5) = P(X=0)+P(X=1)+...+P(X=4)
=14C0*(0.1^0)*(0.9^(14-0))+...+14C4*(0.1^4)*(0.9^(14-4))
=0.9907698
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(4)
Data cumulative lower upper midpoint width frequency percent frequency percent 4 < 9 7 5 5 16.7 5 16.7 9 < 14 12 5 5 16.7 10 33.3 14 < 19 17 5 7 23.3 17 56.7 19 < 24 22 5 8 26.7 25 83.3 24 < 29 26 5 5 16.7 30 100.0 30 100.0