Exam 2. STA 2023-009. Feb 5, 2018 No cell phones or list ening devices are allow

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Exam 2. STA 2023-009. Feb 5, 2018 No cell phones or list ening devices are allowed during the test. A legitimate ec the answers phone or other electronic devices) will be allowed. Time: 50 minutes to scantron and on the test. the recored the answers both on MULTIPLE CHOICE. Choose the one alternative that best completes the statem 1) Let A and B be events with POA) = 0.2, PO»-05, and PCA and Bal independent? A) No B) Yes 2) 2) A poll was taken of 14,056 working adults aged 40-70 to defedcaion. 1 education. The participants were classified by sex and by were as follows. Education Level Male FemaleTotal High School or Less 3141 2434 5575 7380 Bachelor's Degree 3619 3761 aster's Degree 534472 1006 Ph.D. Total 52 43 95 7346 6710 14,056 A person is selected degree. at random. Compute the probability that the person has a master's D) 0.036 B) 0.034 C) 0.038 A) 0.072 3) n unfair coin has a probability 0.4 of landing heads. The coin is tossed two times. What is the probability that it lands heads at least once? D) 0.5 B) 0.64 C) 0.84 A) 0.6 4) non-fiction books, and 253 were videos (of any genre). What is the probability that a randomly-selected item was not a video? 4) Out of 829 items checked out of a public library, 282 were fiction books, 294 were C) 0.340 D) 0.305 A) 0.439 B) 0.695 5) The numbers I through 10 are written in separate slips of paper, and the slips are placed into a box. Then, 4 of these slips are drawn at random. What is the probability that the drawn slips are "I" "2", "3", and "4", in that order? A) 0.00476 B) 0.004752 C) 0.000198 D) 0.11424

Explanation / Answer

1) A and B independent,only if P(A and B) = P(A) P(B)

Here, P(A) = 0.2 & P(B) = 0.5 & P(A and B) = 0.08

P(A) * P(B) = 0.2 * 0.5 = 0.1 which is not equal to 0.08.

Therefore A and B are not independent.

2) Given:-

Total Adults = 14,056

Total Adults having Master's Degree = 1006

We want probability that a person selected at random has Master's Degree,

P(Master's Degree) = Total Adults having Master's Degree / Total Adults

= 1006/14056

= 0.072

Hence answer is option A i.e 0.072

3) Given:-

p = 0.4 is the probability of landing heads

q = 1-p = 1 - 0.4 = 0.6 is the probability of landing tails.

The probability of getting 2 tails in a row is q^2 = (0.6)^2 = 0.6*0.6 = 0.36

Hence to find the probability of landing heads at least once is,

1 - 0.36 = 0.64

Hence answer is option B i.e 0.64

4) Given:-

Total items = 829

We want the probability that a randomly-selected item was not a video,

We can find by, Total video items = 253

Now if we substract 253 from total items we will get the items which are not video

i.e 829 - 253 = 576 are the items wich are not video

The probability that a randomly-selected item was not a video is,

Items which are not video / Total Items = 576 / 829 = 0.695

Hence answer is option B i.e 0.695

  

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