Assignment:
Q1. [DESCRIPTIVE STATISTICS: The following unsorted data shows the number of traffic tickets given each day by Deputy Fife over the last eleven days. Compute the descriptive statistics for the following data and be prepared to answer several questions about the output:
{10, 20, 2, 8, 0, 23, 15, 5, 10, 12, 15 }
Q2. JOINT PROBABILITY: Women who think they might be pregnant will often test themselves using the Home Pregnancy Test. Assuming 200 women tested themselves today; it turns out that 50 were pregnant but the test was obviously not perfect. Be prepared to answer questions regarding joint probabilities as shown by the table below:
Test Positive Test Negative Total
Pregnant 44 6 50
Not Pregnant 30 120 150
Total 74 126 200
EXPECTED VALUE: A company has produced a new line of sweetener that it plans to market. They estimate a 30% probability of losing 50k, a 20% probability of gaining 20k and a 50% probability of earning 100k. Compute the expected value of their profit / loss if they launch the sweetener.
Profit Probability
$- 50,000 .30
$ 20,000 .20
$100,000 .50
Q3. BINOMIAL: Suppose that a website statistics shows that 30% of those who visit the website make a purchase. Assume 20 people visit the website today. Set up the binomial problem and be prepared to answer several questions from the output.
Q4. NORMAL: The mean amount spent by a family on food per month is $500 with a standard deviation of $75. Assuming that the food costs are normally distributed, what is the probability that a family spends more than $410 per month?
Q5. NORMAL: A new extended-life light bulb has an average service life of 750 hours, with a standard deviation of 45 hours. If the service life of these light bulbs approximates a normal distribution, about what percent of the distribution will be between 600 hours and 800?
Q6. NORMAL: A resort tracks the number of days each guest stays. They've discovered that this variable is normally distributed with a mean of 9 days and a standard deviation of 3. They would expect 10% of the guests stay longer than how many days?
Q7. NORMAL-CLT: The average age of Webster online students is known to be 29.2 years with a standard deviation of 2.5 years. If a random sample of 36 online students is selected, what is the probability that the mean age is over 30?
Q8. CONFIDENCE INTERVALS: A survey of 25 grocery stores revealed that the average price of a gallon of milk was $2.98 with a standard deviation of $0.50. What is the 95% confidence interval to estimate the true mean cost of a gallon of milk?
Q9. CONFIDENCE INTERVALS: A sample of 50 Hummer owners revealed that 40 have cut back on their driving due to the increased cost of gasoline. Give a 90% confidence interval for the proportion of Hummer owners who plan to cut back their driving.
Q10. SAMPLE SIZES: A bank wishes to estimate the mean balances owed by their MasterCard customers within $75. The population standard deviation is estimated to be $300. If a 98 percent confidence interval is used, how many cardholders should be sampled?
Q11. SAMPLE SIZES: Comcast wants to know the percent of their cable subscribers who use the internet at home. How large of a sample should they survey to determine the proportion who use the internet within 2% and with 90% confidence?