(1) The following are the amounts from the sales slips of a department store in dollars: 3.45, 4.52, 5.41, 6.00, 5.97, 7.18, 1.12, 5.39, 7.03 10.25, 11.45, 13.21, 12.00, 14.05, 2.99, 3.28, 17.10, 19.28, 2.09, 12.11, 5.88, 4.65, 3.99, 10.10, 23.00, 15.16, 20.16.

Required:

1. Group the data in categories of frequency table
2. Draw a frequency polygon for these data by defining intervals of the data and counting the data points in each interval.
3. Draw a ogive and a column graph

(2) The following is a random sample of 90-day futures prices in dollars for 1 troy oz. of silver from The Wall Street Journal issues in May and June of 1997: 4.74, 4.77, 4.87, 4.91, 4.83, 4.72, 4.92, 4.86, 4.97, 4.71, 4.90, 4.93, 4.75, 4.88, 4.79, 4.83, 4.89.

Required:

1. Calculate the mean
2. Median
3. The standard deviation of the 90-day future price of silver data

(3) An e-commerce Website gets 2,385 visitors on a particular day. Among these, 1790 visitors explore the products by looking at more pages on the site. Among these 1790 visitors who explore the products, 387 make a purchase.

Required:

1. If a visitor is chosen at random from all those who visited the site, what is the probability that the visitor explored the products?
2. If a visitor is chosen at random from all those who visited the site, what is the probability that the visitor made a purchase?
3. If a visitor is chosen at random from all those who explored the products, what is the probability that the visitor made a purchase?
4. Which of the preceding three probabilities is relevant to the design of the home page that leads to the product page.

(4) A financial analyst believes that if interest rates decrease in a given period, then the probability that the stock market will go up is 0.80. The analyst further believes that interest rates have a 0.40 chance of decreasing during the period in question. Given the above information, what is the probability that the market will go up and interest rates will go down during the period in question?

(5) An investment analyst collects data on stocks and notes whether or not dividends were paid and whether or not the stocks increased in price over a given period. Data are presented in the following table:

	Price Increase	No price Increase	Total
Dividends paid	34	78	112
No dividends paid	85	49	134
Total	119	127	246

1. If a stock is selected at random out of the analyst list of 246 stocks, what is the probability that it increased in price?
2. If a stock is selected at random, what is the probability that it paid dividends?
3. If a stock is randomly selected, what is the probability that it both increased in price and paid dividends?
4. What is the probability that a randomly selected stock neither paid dividends nor increased in price?
5. Given that stock increased in price, what is the probability that it also paid dividends?
6. If a stock is known not to have paid dividends, what is the probability that it increased in price?
7. What is the probability that a randomly selected stock was worth holding during the period in question; that is, what is the probability that it increased in price or paid dividends or did both.

(6) A mining company needs to estimate the average amount of copper ore per ton mined. A random sample of 50 tons gives a sample mean of 146,75 pounds. The population standard deviation is assumed to be 35.2 pounds.

Required:

1. Give a 95% confidence interval for the average amount of copper in the population of tons mined.
2. Give a 90% confidence interval for the average amount of copper per ton
3. Give a 99% confidence interval for the average amount of copper per ton

(7) A pharmaceutical manufacturer wants to determine the concentration of a key component of cough medicine that may be used without the drug's causing adverse effects. As part of the analysis, a random sample of 45 patients is administered doses of varying concentration (X), and the severity of side effects (Y) is measured. The results include