Probability: Normal Distribution and Null Hypothesis

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%