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Statistics and Probability Part 1: Mechanical Engineer Board Exam Review

Here are some review questions in Mathematics, Statistics and Probability.

Instruction: Choose the BEST answer.

Mechanical Engineering Board Exam Review: Statistics and Probability part 1

1. In how many ways can you arrange a group of 5 girls and 3 boys in 7 vacant chairs?
a. 40320
b. 5040
c. 720
d. 8

2. How many 3-digit numbers can you make out of the numbers 1 to 5 without repetition?
a. 720
b. 10
c. 60
d. 120

3. There are 2 white, 3 red, and 4 blue balls inside a basket. If three balls are drawn randomly in succession without replacement, what is the probability that the first ball is white, and the next two balls are blue?
a. 32/729
b. 4/63
c. 8/243
d. 1/21

4. What is the mode of the following numbers: 54, 45, 75, 60, 65, 65, 60, and 57?
a. 65
b. 60
c. 62.5
d. 60 and 65

5. From the given numbers of question number 4, what is the median?
a. 65
b. 60
c. 62.5
d. 60 and 65

6. From the given numbers of question number 4, what is the variance?
a. 77.84
b. 60.125
c. 68.11
d. 8.82

7. Seven boys are to be seated around a circular table. How many arrangements can be made?
a. 7
b. 2520
c. 5040
d. 720

8. In how many ways can you arrange 3 boys and 4 girls in a 7-seater bench supposing that the four girls want to be seated together?
a. 24
b. 5040
c. 576
d. 48

9. The probability that you will arrive late is 35% and the probability that you will scolded by your boss is 15%. What is the probability that you will be both late and scolded by your boss?
a. 5.25%
b. 50%
c. 44.75%
d. 2.33%

10. From question number 9, what is the probability that you will either be late or scolded by your boss?
a. 5.25%
b. 50%
c. 44.75%
d. 2.33%

If you noticed a question with no correct answer in the option or the question itself seems to be erroneous, I would appreciate if you can send me an email or comment below. Computation-type review questions are very hard to do and requires extensive validation. I would appreciate any help for the improvement of this blog. Thanks!

Answers will be posted after a week.


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