Please show steps Thanks 1 At a college 70 percent of the st

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

Solution

(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)