1. Consider the following: x P(x) -2 -0.5 -1 0 0 0.2 1 0.2 2 0.1 IF the above distribution is a probability distribution then compute its mean. Otherwise please state NOT A PROBABILITY DISTRIBUTION . 2. According to data from the American Medical Association 10% of people are left-handed. In a group of 5 people find the probability that (a) exactly 1 is left-handed. (b) at least 2 are left-handed. (c) at most 4 are right-handed. 3. Assume that the readings on a thermometer form a standard normal distribution. A thermometer is randomly selected. Find each of the following probabilities. (a) thermometer s reading is between 0 and 1. (b) thermometer s reading is greater than 0.5. (c) thermometer s reading is less than 0. 4. IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. Mensa is an organization for people with high IQ s and eligibility requires an IQ above 131.5. (a) If someone is randomly selected find the probability that he or she meets the requirement. (b) If 5 people are randomly selected find the probability that the mean of their IQ s meets the requirement. 5. Let s suppose you have been falling in love with Japan and during your love affair with Japan you decide to open up a new branch of Konaka men s Clothing Store. Suppose that men in your community have a mean height of 69 in. and a standard deviation of 2.8 in. To minimize start-up costs you decide to not stock suits for the tallest 5% and the shortest 5% of men. Find the minimum and maximum heights of the men for whom suits will be stocked. 6. A NAPA Auto Parts supplier wants information about how long car owners plan to keep their cars. A random sample of 25 car owners results in mean 7.1 years and s = 3.74 years respectively (based on data from a Roper poll). Assuming that the sample is drawn from a normally distributed population find a 95% confidence interval for the population mean. 7. An economist wants to estimate the mean income for the first year of work for a college graduate who has had the profound wisdom to take a statistics course. How many such incomes must be found if we want to be 99% confident that the sample mean is within $500 of the true population mean? Assume that a previous study has revealed that for such incomes = 6250 . 8.When Mendel conducted his famous genetics experiments with peas one sample of offspring consisted of 428 green peas and 152 yellow peas. (a) Find a 95% confidence interval estimate of the percentage of yellow peas. (b) Based on his theory of genetics Mendel expected that 25% of the offspring peas would be yellow. Given that the percentage of offspring yellow peas is not 25% do the results contradict Mendel s theory? Why or why not? 9. In the course of designing theater seats the sitting heights (in mm) of a sample of adult women is obtained and the results are listed below. Use the sample data to construct a 95% confidence interval estimate of (population standard deviation) the standard deviation of sitting heights of all women. Does the confidence interval contain the value of 35 mm which is believed to be the standard deviation of sitting heights of women? 849 807 821 859 864 877 772 848 802 807 887 815 10. With the popularity of Facebook one could theoretically monitor a particular person s popularity. So your friendly instructor has chosen 10 of his Facebook friends and recorded the number of friends that each of those 10 friends have. They are 325 246 81 978 1415 288 3459 344 108 590. At a significance level of .01 can it be concluded that the mean number of friends is more than 500. 11. Do cars on eastbound Interstate 10 near the Louisiana-Texas border travel slower than the cars in westbound Interstate 10 near the Louisiana-Texas border? If so then perhaps more people are looking forward to going to Texas rather than going to Louisiana. Hahahaha. So for 3 months data consisting of rates in miles per hour of cars were collected and the mean and standard deviation of those rates were tabulated. Here are the results: EASTBOUND WESTBOUND = 75 = 78 s = 3.2 s = 5 n = 60 n = 40 Can it be concluded that people in eastbound Interstate 10 drive slower than people in westbound Interstate 10? Use a significance level of 0.1. 12. To test the effectiveness of a violin lesson a teacher gives randomly selected students a pretest and a follow-up test. The results below are based on a scale from 0 (worst) to 10 (best). Student A B C D E F G H Before 6 8 5 4 3 5 4 7 After 4 10 5 7 0 8 5 6 At the 0.05 level of significance can it be concluded that the lesson improved scores overall?
