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# Short problems related to probability distributions

1. A furniture manufacturer offers bookcases in 5 different sizes and 3 different colors. If every color is available in every size, then the total number of different bookcases is

A) 5
B) 8
C) 15
D) 30

2.A certain system has two components. There are 10 different models of the first component and 10 different of the second. Any first component can be paired with any second component. A salesman must select 2 of the first component and 3 of the second to take on a sales call. How many different systems can the salesman select? Place your answer in the blank. Do NOT use commas. ___________________

3. What probability value would be needed to complete the following probability distribution?

X -2 -1 0 1 2
P(X) 0.13 0.14 0.16 0.29

4.The probability distribution associated with the number of cartoons watched by Mrs. Kelly's first grade class on Saturday morning is shown below.

0 0.15
1 0.20
2 0.30
3 0.10
4 0.20
5 0.05

Find the standard deviation for the probability distribution above.

A)1.46
B)2.25
C)1.89
D)1.18

5.If a student randomly guesses at 20 multiple-choice questions, find the probability that the student gets exactly four correct. Each question has four possible choices.

A)0.19
B)0.17
C)1.08
D) 0.23

6.If 1.5% of the bolts made by an automotive factory are defective, what is the probability that in a shipment of 200 bolts, there are 6 defective bolts? Place your answer, rounded to four decimal places, in the blank. ____________.

7.A multiple choice quiz consists of 6 questions, each with 4 possible answers. If a student guesses at the answer to each question, then the mean number of correct answers is

A)6.00
B)1.50
C)4.00
D) 10.00

8.The failure rate for taking the bar exam in Philadelphia is 41%. If 375 people take the bar exam, what is the mean for the number of failures?

A) 138.1
B) 171.2
C) 90.7
D) 153.8

9.In a survey, 55% of the voters support a particular referendum. If 40 voters are chosen at random, and X is the number of voters that support this referendum, find the mean and variance of X. Place the mean in the first blank ____________ and place the variance in the second blank. ______________

#### Solution Preview

Please see the attached file for complete solution and better clarity.

1.A furniture manufacturer offers bookcases in 5 different sizes and 3 different colors. If every color is available in every size, then the total number of different bookcases is

A) 5
B) 8
C) 15
D) 30

2.A certain system has two components. There are 10 different models of the first component and 10 different of the second. Any first component can be paired with any second component. A salesman must select 2 of the first component and 3 of the second to take on a sales call. How many different systems can the salesman select? Place your answer in the blank. Do NOT use commas. __5400________________

total systems = 10C2*10C3 = 120*45 =5400

n!
n_C_k = ----------
k!(n - k)!

10C2 =10!/(2!*8!)= 10*9/2 = 45

10C3 = 10!/(3!*7!) = 10*9*8/3*2*1 = 120

3. What probability value ...

#### Solution Summary

There are 9 short quantitative problems related to discrete probability distribution. Steps have been explained to calculate mean, variance and standrad deviation of probability distribution.

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