5 - STAT 350 Fall 2008 Homework #5 Solution through Lecture...

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

View Full Document Right Arrow Icon
STAT 350 – Fall 2008 Homework #5 – Solution through Lecture #9 Text Exercises Chapter 7, Problem #30 7.30 () 22 4.89 6.43 26.99 35.76 1.96 68 74 −± + = (-10.6401, -6.8999) Note: (6.8999, 10.6401) is also acceptable, this is just the 95% CI for 21 μ instead of 12 Then answer the following problems 1. According to www.mms.com , 20% of milk chocolate M&M's are red. Sally will eat one snack pack of milk chocolate M&M's, for a total of 23 M&M's. Let p 1 denote the proportion of M&M's Sally will eat that are red. a. What is the expected value of p 1 ? E( p 1 ) = π = 0.20 b. What is the standard deviation of p 1 ? 2 1 0.2 1 0.2 0.0834058 23 SD p n ππ −− == = c. Find the exact probability that p 1 < 0.15. Hint: you should not be using the normal distribution for this problem! We cannot assume that p 1 is approximately normally distributed, because n π = 4.6 < 5 . What we can do instead is to convert the question to a question about the number of red M&M's in the bag, and answer the question using the Binomial distribution. For p 1 to equal 0.15, there would have to be 0.15(23) = 3.45 red M&M's in the bag. Any less than that and p 1 will be less than 0.15. Let X = the number of red M&M's in this bag X ~ Binomial(n = 23, π = 0.20) We need to find P( X < 3.45) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3).
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/23/2009 for the course STAT 350 taught by Professor Staff during the Fall '08 term at Purdue University.

Page1 / 4

5 - STAT 350 Fall 2008 Homework #5 Solution through Lecture...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online