statistics problems

1.         It is estimated that 27% of all California adults are college graduates and that 31% of California adults are regular internet users. It is also estimated that 21% of California adults are both college graduates and regular internet users.(a) Among California adults, what is the probability that a randomly chosen internet user is a college graduate? Round your answer to 2decimal places.(b) What is the probability that a California adult is an internet user, given that he or she is a college graduate? Round your answer to 2 decimal places.2. A soft drink company has recently received customer complaints about its one-liter-sized soft drink products. Customers have been claiming that the one-liter-sized products contain less than one liter of soft drink. The company has decided to investigate the problem. According to the company records, when there is no malfunctioning in the beverage dispensing unit, the bottles contain 1.01liters of beverage on average, with a standard deviation of 0.14liters. A sample of 70bottles has been taken to be measured from the beverage dispensing lot. The mean amount of beverage in these 70bottles was 0.995liters. Find the probability of observing a sample mean of 0.995liters or less in a sample of 70bottles, if the beverage dispensing unit functions properly.Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.3. An existing inventory for a test measuring self-esteem indicates that the scores have a standard deviation of 8 . A psychologist gave the self-esteem test to a random sample of 70individuals, and their mean score was 68 . Construct a 95%confidence interval for the true mean of all test scores. Then complete the table below.Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place.This goes with question 3What is the lower limit of the 95% confidence interval?What is the upper limit of the 95% confidence interval?4. Use the calculator provided to solve the following problems.Consider a t distribution with 15degrees of freedom. Compute P(t > 1.33). Round your answer to at least three decimal places.Consider a t distribution with 18degrees of freedom. Find the value of c such thatP(-cc) = 0.1. Round your answer to at least two decimal places.

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