I need Help with Engineering Statics Homework

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I want to help with these questions for homework using an Excel. I attach the file for the homework you see all the requirements for the home

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β€’ β€’ On questions requiring a numerical answer, show how the answer was obtained by Excel files. Answer all sub questions (if any) of a problem for full credit for that problem. Exercise 3-95 on Page 101 Customers purchase a particular make of automobile with a variety of options. The probability mass function of the number of options is x 7 8 9 10 11 12 13 𝑓(π‘₯) 0.040 0.130 0.190 0.240 0.300 0.050 0.050 (a) What is the probability that a customer will choose fewer than 9 options? (b) What is the probability that a customer will choose more than 11 options? (c) What is the probability that a customer with choose between 8 and 12 options, inclusively? (d) What is the expected number of options chosen? What is the variance? Exercise 3-130 on page 117 Flaws occur in Mylar material according to a Poisson distribution with a mean of 0.01 flaw per square yard. (a) If 25 square yards are inspected, what is the probability that there are no flaws? (b) What is the probability that a randomly selected square yard has no flaws? (c) Suppose that the Mylar material is cut into 10 pieces, each being 1 yard square. What is the probability that 8 or more of the 10 pieces will have no flaws? Hint: Let V denote the number of square yards out of 10 that contain no flaws. Then, V is a binomial random variable with n = 10 and 𝑝 = 𝑃(π‘Œ = 0) (from part (b). Exercise 3-148 on page 122 A large electronic office product contains 2000 electronic components. Assume that the probability that each component operates without failure during the useful life of the product is 0.995, and assume that the components fail independently. Approximate the probability that 5 or more of the original 2000 components fail during the useful life of the product. Exercise 3-160 on page 128 Let X be an exponential random variable with mean equal to 5 and Y be an exponential random variable with mean equal to 8. Assume X and Y are independent. Find the following probabilities. (a) (b) (c) (d) 𝑃(𝑋 ≀ 5, π‘Œ ≀ 8) 𝑃(𝑋 > 5, π‘Œ ≀ 6) 𝑃(3 < 𝑋 ≀ 7, π‘Œ >) 𝑃(𝑋 > 7, 5 < π‘Œ ≀ 7) Exercise 3-175 on page 135 If X1 and X2 are independent random variables with πœ‡1 = 6, πœ‡2 = 1, 𝜎1 = 2, 𝜎2 = 4, and π‘Œ = 4𝑋1 βˆ’ 2𝑋2 , determine the following (a) (b) (c) (d) 𝐸(π‘Œ) 𝑉(π‘Œ) 𝐸(2π‘Œ) 𝑉(2π‘Œ) Exercise 3-198 on page 140 Intravenous fluid bags are filled by an automated filling machine. Assume that the fill volumes of the bags are independent, normal random variables with a standard deviation of 0.08 fluid ounce. (a) What is the standard deviation of the average fill volume of 20 bags? (b) If the mean fill volume of the machine is 6.16 ounces, what is the probability that the average fill volume of 20 bags is below 5.95 ounces? (c) What should the mean fill volume equal in order that the probability that the average of 20 bags is below 6 ounces is 0.001? ...
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Tutor Answer

svantass
School: Boston College

Here are both files :) Let me know if you need anything else

β€’
β€’

On questions requiring a numerical answer, show how the answer was obtained by
Excel files.
Answer all sub questions (if any) of a problem for full credit for that problem.

Exercise 3-95 on Page 101
Customers purchase a particular make of automobile with a variety of options. The
probability mass function of the number of options is
x

7

8

9

10

11

12

13

𝑓(π‘₯)

0.040

0.130

0.190

0.240

0.300

0.050

0.050

(a) What is the probability that a customer will choose fewer than 9 options?
P(7)+P(8) = 0.040 + 0.130 = 0.17
(b) What is the probability that a customer will choose more than 11 options?
P(12)+P(13) = 0.050 + 0.050 = 0.1
(c) What is the probability that a customer will choose between 8 and 12 options,
inclusively?
P(8)+P(9)+P(10)+P(11)+P(12) = 0.91
(d) What is the expected number of options chosen? What is the variance?
E(X)=7(.04)+8(.13)+9(.19)+10(.24)+11(0.3)+12(.05)+13(.05) = 9.98
Var(x) = βˆ‘7𝑖=1 𝑝(π‘₯𝑖 )(π‘₯𝑖 βˆ’ 9.98)2 = 2.0196

Exercise 3-130 on page 117
Flaws occur in Mylar material according to a Poisson distribution with a mean of 0.01 flaw
per square yard.
(a) If 25 square yards are inspected, what is the probability that there are no flaws?
P(0, .25) =

𝑒 βˆ’.25 .250
0

= 0.77880078

(b) What is the probability that a randomly selected square yard has no flaws?
P(0,0.01) =

𝑒 βˆ’0.01 0.010
0!

=.99004983

(c) Suppose that the Mylar material is cut into 10 pieces, each being 1 yard square.
What is the probability that 8 or more of the 10 pieces will have no flaws? Hint:
Let V denote the number of square ...

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