STA 301 - HW08 Key - STA 301 Applied Statistics Spring 2008...

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

View Full Document Right Arrow Icon
-3 -2 -1 0 1 2 3 .1736 .0735 .7529 STA 301 – Applied Statistics Spring 2008, Section B Homework #8 - Key Due Friday, April 4 Question 1 (p. 252, #8.22) The heights of 1000 students are approximately normally distributed with a mean of 174.5 centimeters and a standard deviation of 6.9 centimeters. If 200 random samples of size 25 are drawn from this population, determine (a) the mean and standard deviation of the sampling distribution of X In the population we have and . Since we are taking samples of size n = 25, we have: and (b) the number of sample means that are expected to fall between 172.5 and 175.8 centimeters First, we find the probability of the sample mean falling between 172.5 and 175.8: Now, let Y be a random variable representing the number of our 200 samples of size 25 that have means between 172.5 and 175.8. Then Y is binomial with 200 trials and probability of success .7529. The number of sample means expected to fall between 172.5 and 175.8 is therefore: 200 * .7529 = 150.58 5 . 174 = X μ 9 . 6 = X σ 5 . 174 = = X X μ μ 38 . 1 25 9 . 6 = = = n X X σ σ ( ( 29 ( 29 ( 29 7529 . 1736 . 0735 . 1 94 . 45 . 1 1 94 . 45 . 1 38 . 1 5 . 174 8 . 175 38 . 1 5 . 174 5 . 172 8 . 175 5 . 172
Image of page 1

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

View Full Document Right Arrow Icon
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