27 x 130 101 27 p 059z107pz107 pz 059 08577

This preview shows page 110 - 117 out of 187 pages.

=P(8.5≤X≤13.0)=P( 8.5 10.1 2.7 ≤ X ≤ 13.0 10.1 2.7 )=P(-0.59≤Z≤1.07)=P(Z≤1.07)-P(Z≤- 0.59) =0.8577-0.2776=0.5801. b) 0.5801 is the proportion of the product having maximum attenuation between 8.5 and 13.0 dB c) Proportion of the products having maximum attenuation greater than 15.1 dB =P(X>15.1)=P(Z>(15.1-10.1)/(2.7))=P(Z>1.85)=1-0.9678=0.0322 Problems to be discussed by the faculty: 1. Given a Standard Normal distribution, find the area under the curve which lies a) To the left of z=1.43; b) to the right of z=-0.89 c) between z=-2.16 and z=-0.65 d) to the left of z=-1.39 e) to the right of z=1.96 f) between z=-0.48 and z= -1.74
Image of page 110

Subscribe to view the full document.

111 2. Given a standard normal distribution find the value of k such that a) P ( z < k ) = 0.0427 ; b) P ( z > k ) = 0.2946 ; c) P(-0.93<Z<k)=0.7235.
Image of page 111
112 Tutorial: 1.Given the normally distributed variable X with mean 18 and standard deviation 2.5, find a) P(X<15); b) the value of k such that P(X<k)=0.2236; c) the value of k such that P(X>k)=0.1814; d) P(17<X<21).
Image of page 112

Subscribe to view the full document.

113 Session: 12 Uniform distribution: Tutorial problems: 1. Find the distribution of a random variable having a uniform distribution on [0,1] 2. In a certain experiments, the error made in determining the solubility of a substance is a random variable having the uniform density with A=-0.025 and B=0.025. What are the probabilities that such an error will be a) Between 0.010 and 0.015 b) Between -0.012 and 0.012?
Image of page 113
114 Homework: 1. From experience Mr. Harris has found that the low bid on a construction job can be regarded as a random variable having the uniform density f ( x ) = { 3 4 c ,for 2 c 3 < x < 2 c 0, elsewhere Where c is his own estimate of the cost of the job, what percentage should Mr. Harris add to his cost estimate when submitting bids to maximize his expected profit?
Image of page 114

Subscribe to view the full document.

115 MATLAB Commands: y=unifpdf(x,a,b) Computes the continues Uniform pdf at the given value of x using the corresponding lower end point (minimum) a and upper end point (maximum) b. Y=unifcdf(x,a,b) compute the cumulative distribution function of x using the corresponding lower end point and upper end point. With reference to the above Example- MATLAB Code: >> y=unifcdf(15,0,30)+unifcdf(30,0,30)-unifcdf(20,0,30); >>fprintf('\n probability that the passenger waits more than 5 minutes for a bus=%.4f\n',y) probability that the passenger waits more than 5 minutes for a bus=0.8333 Exponential distribution: Tutorial: 1. The life, in years, of a certain type of electrical switch has an exponential distribution with an average life β=2. If 100 of these switches are installed in different systems, what is the probability that at most 30 fail during the first year?
Image of page 115
116 2. Suppose that a study of a certain computer system reveals that the response time, in seconds, has an exponential distribution with a mean of 3 seconds. a) What is the probability that response time exceeds 5 seconds? b) What is the probability that response time is less than 10 seconds? c) What are the mean and variance of response time? 3. The density function of the time Z in minutes between calls to an electrical supply store is given by f ( Z ) = { 1 10 e z 10 0, elsewhere , 0 < z < a) What are the mean and variance of time between calls?
Image of page 116

Subscribe to view the full document.

Image of page 117

{[ snackBarMessage ]}

Get FREE access by uploading your study materials

Upload your study materials now and get free access to over 25 million documents.

Upload now for FREE access Or pay now for instant access
Christopher Reinemann
"Before using Course Hero my grade was at 78%. By the end of the semester my grade was at 90%. I could not have done it without all the class material I found."
— Christopher R., University of Rhode Island '15, Course Hero Intern

Ask a question for free

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern