Sloution to problem set 6

Probability and Statistics for Engineering and the Sciences (with CD-ROM and InfoTrac )

Info icon This preview shows pages 1–2. Sign up to view the full content.

Sol6 1. a. P(0 Z 2.17) = Φ (2.17) - Φ (0) = .4850 b. Φ (1) - Φ (0) = .3413 c. Φ (0) - Φ (-2.50) = .4938 d. Φ (2.50) - Φ (-2.50) = .9876 e. Φ (1.37) = .9147 f. P( -1.75 < Z) + [1 – P(Z < -1.75)] = 1 - Φ (-1.75) = .9599 g. Φ (2) - Φ (-1.50) = .9104 h. Φ (2.50) - Φ (1.37) = .0791 i. 1 - Φ (1.50) = .0668 j. P( |Z| 2.50 ) = P( -2.50 Z 2.50) = Φ (2.50) - Φ (-2.50) = .9876 2. a. .9838 is found in the 2.1 row and the .04 column of the standard normal table so c = 2.14. b. P(0 Z c) = .291 ⇒Φ (c) = .7910 c = .81 c. P(c Z) = .121 1 - P(c Z) = P(Z < c) = Φ (c) = 1 - .121 = .8790 c = 1.17 d. P(-c Z c) = Φ (c) - Φ (-c) = Φ (c) – (1 - Φ (c)) = 2 Φ (c) – 1 ⇒Φ (c) = .9920 c = .97 e. P( c | Z | ) = .016 1 - .016 = .9840 = 1 – P(c | Z | ) = P( | Z | < c ) = P(-c < Z < c) = Φ (c) - Φ (-c) = 2 Φ (c) – 1 ⇒Φ (c) = .9920 c = 2.41 3. a. Φ (c) = .9100 c 1.34 (.9099 is the entry in the 1.3 row, .04 column) b. 9 th percentile = -91 st percentile = -1.34 c. Φ (c) = .7500 c .675 since .7486 and .7517 are in the .67 and .68 entries, respectively.
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

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