Probabilities

A. Scores of high school students on a national mathematics exam in Egypt were normally distributed with a mean of 86 and a standard deviation of 4. 1. What is the probability that a randomly selected student will have a score of 80 or higher? 2. If there were 97,680 students with scores higher than 91, how many students took the test? B. In a study of television viewing habits among married couples, a researcher found that for a popular Saturday night program, 25% of the husbands viewed the program regularly and 30% of the wives viewed the program regularly. The study found that, for couples where the husband watches the program regularly, 80% of the wives also watch regularly. What ... click for more

Probabilities

An ice cream vendor sells three flavors: chocolate, strawberry, and vanilla. Forty five percent of the sales are chocolate, while 30% are strawberry, with the rest vanilla flavored. Sales are by the cone or the cup. The percentages of cones sales for chocolate, strawberry, and vanilla, are 75%, 60%, and 40%, respectively. For a randomly selected sale, define the following events: A1 = chocolate chosen A2 = strawberry chosen A3= vanilla chosen B = ice cream on a cone Bc = ice cream in a cup a. Find the probability that the ice cream was sold on a cone and was vanilla flavor, b. Find the probability that the ice cream was sold in a cup. c. Find the probabilit... click for more

Confidence intervals

The manager of a local bank wants to estimate the average amount held in checking accounts by the customers. A random sample of 30 customers is selected, and the results indicate a sample average of $4,750 and a sample standard deviation of $1,200. a) Set a 95% confidence interval estimate of the average amount held in all checking accounts. b) Test the hypothesis that the true average of the population is $4,000, against the hypothesis that it's different.

Regression and Probability

Please see the attached file. You have on the following page, data on two variables. The first, gdp, is US Gross Domestic Product, and the second, receipts, is total tax receipts of the federal government. The variables are measured annually from 1960 to 1995.... (see attachment)

Regression - probability of the error (STATA)

1. Yes, we use STATA to test. 2. Tax is the dependent variable: tax = B1 + B2income + e The gross income and tax paid by a cross-section of 30 companies in 1988 and 1989 is given in the file tax.dta Consider the estimate for B2 for 1989 and the corresponding estimated variance. Pretend that the estimated variance is the same as the true variance var(b2), and assume that b2 is normally distributed. Find the probability that the sampling |b2 − B2| is (i) less than 0.04 and (ii) less than 0.01.