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Solve the following problems in essay form (1 to 2 paragraphs for each problem is fine). Please show all work and show how you came up with the answer. Please make sure that you address the following questions: (1) How did you get your answer? (2) What steps did you take? (3) Where did you begin? (4) Why did you do what you did? (5) Explain in detail what your answers to the problems are?
Problem 1 -
Mr. Smith invited 17 guests to his "Disco-reunion" party. He assigned each guest a number from 2 to 18, keeping 1 for himself. When everyone was dancing, he noticed that the sum of each couple's numbers was a perfects square. What was he number of Mr. Smith's partner?
Problem 2 -
Define "prime date" to be a date during the year where both the months (as a number, i.e. January is 1, February is 2, etc) and the day are both prime numbers. What is the average number of prime dates per week in one year?
A committee of three is selected at random from a set consisting of five Democrats, eight Republicans, and two Independents.
Systolic blood pressures are measured at baseline and again 4 weeks later. Compute a 95% confidence interval for the mean difference in blood pressure over 4 weeks.
Compute a 95% confidence interval for the mean saline of the tears. You select a random sample of 100 tear drops. The sample has an average salt concentration of 0.1 with a standard deviation of 0.01.
Given that the mean of 100 observations is 42.5 and that their standard deviation is 6.313, find the sum of the squares of the observations.
For a binomial probability experiment, with n=150 and p=.2, it is appropriate to use the normal approximation to the binomial distribution.
Calculate the standard error of estimate for the regression equation.
The Federal Government is stepping up efforts to reduce average response times of fire departments to fire calls. The distribution of mean response times to fire calls follows a normal distribution with a mean of 12.8 minutes and a standard deviat..
Hugger Polls contends that an agent conducts a mean of 53 in-depth home surveys every week. A streamlined survey form has been introduced, and Hugger wants to evaluate its effectiveness.
Given the following revenue and cost function for a business firm, calculate the break-even quantity, total revenue, total cost and total profit at break-even level of production.
The following frequency distribution was obtained. The data values are in hours. Construct a histogram for the data .
In the Willow Brook National Bank waiting line system (see Problem 1), assume that the service times for the drive-up teller follow an exponential probability distribution with a service rate of 36 customers per hour or 0.6 customer per minute.
Suppose you know that the distribution of sample proportions of nonresidents in samples of 200 students is normal with a mean of 0.04 and a standard deviation of 0.03.
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