# Probability: Normal Distribution and Null Hypothesis

Pages: 2 (819 words) Published: October 14, 2012
Homework 3   Probability   1.    As part of a Pick Your Prize promotion, a store invited customers to choose which of three prizes they’d like to win.  They also kept track of respondents’ gender.  The following contingency table shows the results:    | MP3 Player| Camera| Bike| Total| Men| 62| 117| 60| 239|

Woman| 101| 130| 30| 261|
Total| 163| 247| 90| 500|
What is the probability that: a.    a randomly selected customer would pick the camera? 247/500= 0.494= 49.4%b.    A randomly selected woman would pick the camera? 130/261=0.498=49.8%c.    A randomly selected customer would be both male and choose the bike? 60/500=0.12=12% d.    A randomly selected man would choose either the camera or the bike? 177/239=0.74=74%  2.    a. Which part(s) of question 1 above deal with joint probability?  C,b. Which part(s) deal with conditional probability?  B,D   The Standard Normal Curve   3.   In a recent year, about two-thirds of U.S. households purchased ground coffee.  Consider the annual ground coffee expenditures for households who purchase coffee, assuming that these expenditures are approximately normally distributed with a mean of \$45.16 and a standard deviation of \$10.00.       a.   Find the probability that a household spent less than \$25.00.   Z=(25-45.16)/10= -2.016 =.4778=2.2%       b.   Find the probability that a household spent more than \$50.00 (50-45.16)/10=.484=18.44%       c.   What proportion of households spent between \$30.00 and \$40.00?   20.09%       d.   99% of households spent less than what amount?15.16   4.   The breaking strength of plastic bags used for packaging produce is normally distributed, with a mean of 5 pounds per square inch and a standard deviation of 1.5 pounds per square inch.  What proportion of bags have a breaking strength of:       a.   less than 3.17 pounds per square inch?11.12%       b.   at least 3.6 pounds per square inch? 67.67      c.   between 5 and 5.5 pounds per square inch?12.93%...