1. An online stock trading company makes part of their revenue from clients when the clients trade stocks therefore, it is important to the company to have an good idea of how many trades its clients are making in a given year. In a sample of 111 clients of an online stock trading company, the average number of trades per year was 89 with a standard deviation of 18. If you were to test the hypothesis that the average number of trades per year is different than the previous year when the average number of trades was 85 (using the % level of significance), what is the test statistic? (please round your answer to 2 decimal places)
2. There were many car accidents following the snow in Little Rock on Jan. 6. An insurance company who offers automobile insurance had the following number of claims for the following amounts: 26 claims of $500, 13 claims of $1000, 10 claims of $1700, 6 claims of $2300 and 3 claim of $3600. What was the average claim size? (please round your answer to 1 decimal place)
3. Suppose a company rates it employees on a 1-4 scale (with 4
being the highest rating) and the following probability
distribution describes the distribution of the ratings:
27% of the employees had a "4"; 29% of the employees had a "3" rating; 21% of the employees had a "2" rating; and the remaining employees recieved a "1" rating.
What is the expected value of the rating of a randomly chosen employee? (please express your answer using 2 decimal places)
4. In the past, the value of houses a local realtor has sold is normally distributed with a mean of $252,000 with a standard deviation of $85,000. What is the probability that over the next 38 houses the realtor sells, the mean value is less than $240,000? (please round your answer to 4 decimal places)
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