Exam 20: Probability and Combinatorics

The bootstrap confidence interval estimate for the population mean is constructed based on the sampling distribution of the m population means.

SCENARIO 5-12 Two different designs on a new line of winter jackets for the coming winter are available for your manufacturing plants. Your profit (in thousands of dollars) will depend on the taste of the consumers when winter arrives. The probability of the three possible different tastes of the consumers and the corresponding profits are presented in the following table. Probability Taste Design A Design B 0.2 more conservative 180 520 0.5 no change 230 310 0.3 more liberal 350 270 -Referring to Scenario 5-12, if you decide to choose Design A for half of the production lines and Design B for the other half, what is your expected profit?

SCENARIO 5-11 There are two houses with almost identical characteristics available for investment in two different neighborhoods with drastically different demographic composition. The anticipated gain in value when the houses are sold in 10 years has the following probability distribution: -Referring to Scenario 5-11, what is the expected value gain if you invest in both houses?

SCENARIO 9-14 An appliance manufacturer claims to have developed a compact microwave oven that consumes a population mean of no more than 250 W. From previous studies, it is believed that power consumption for microwave ovens is normally distributed with a population standard deviation of 15 W. If there is evidence that the population mean consumption is greater than 250 W, the manufacturer will be unable to make the claim. -Referring to Scenario 9-14, if you select a sample of 20 compact microwave ovens and are willing to have a level of significance of 0.05, the power of the test is _____ if the mean power consumption of all such microwave ovens is in fact 257.3 W.

The amount of time between successive TV watching by first graders follows an exponential distribution with a mean of 10 hours. The probability that a given first grader spends more than 5 hours between successive TV watching is ______.

SCENARIO 5-11 There are two houses with almost identical characteristics available for investment in two different neighborhoods with drastically different demographic composition. The anticipated gain in value when the houses are sold in 10 years has the following probability distribution: -Referring to Scenario 5-11, if you can invest 10% of your money on the house in neighborhood A and the remaining on the house in neighborhood B, what is the portfolio risk of your investment?

A study is under way in Yosemite National Forest to determine the adult height of American pine trees. Specifically, the study is attempting to determine what factors aid a tree in reaching heights Greater than 60 feet tall. It is estimated that the forest contains 25,000 adult American pines. The Study involves collecting heights from 250 randomly selected adult American pine trees and Analyzing the results. Identify the variable of interest in the study.

In the current data-driven environment of business, the decisions you make will be increasingly based on gut or intuition supported by personal experience.

SCENARIO 12-20 The director of the MBA program of a state university wanted to know if a one week orientation would change the proportion among potential incoming students who would perceive the program as being good. Given below is the result from 215 students' view of the program before and after the orientation. -Referring to Scenario 12-20, what is the p-value of the test statistic using a 5% level of significance?

SCENARIO 5-11 There are two houses with almost identical characteristics available for investment in two different neighborhoods with drastically different demographic composition. The anticipated gain in value when the houses are sold in 10 years has the following probability distribution: -Referring to Scenario 5-11, if your investment preference is to minimize the amount of risk that you have to take and do not care at all about the expected return, will you choose a portfolio that will consist of 10%, 30%, 50%, 70%, or 90% of your money on the house in neighborhood A and the remaining on the house in neighborhood B?

Most analysts focus on the cost of tuition as the way to measure the cost of a college education. But incidentals, such as textbook costs, are rarely considered. A researcher at Drummand University wishes to estimate the textbook costs of first-year students at Drummand. To do so, She monitored the textbook cost of 250 first-year students and found that their average textbook Cost was $600 per semester. Identify the variable of interest to the researcher.

SCENARIO 5-14 An accounting firm in a college town usually recruits employees from two of the universities in town. This year, there are fifteen graduates from University A and five from University B and the firm decides to hire six new employees from the two universities. -Referring to Scenario 5-14, what is the probability that at least two of the new employees will be from University B?

SCENARIO 5-11 There are two houses with almost identical characteristics available for investment in two different neighborhoods with drastically different demographic composition. The anticipated gain in value when the houses are sold in 10 years has the following probability distribution: -Referring to Scenario 5-11, if you can invest 70% of your money on the house in neighborhood A and the remaining on the house in neighborhood B, what is the portfolio risk of your investment?

SCENARIO 5-11 There are two houses with almost identical characteristics available for investment in two different neighborhoods with drastically different demographic composition. The anticipated gain in value when the houses are sold in 10 years has the following probability distribution: -Referring to Scenario 5-11, if you can invest 90% of your money on the house in neighborhood A and the remaining on the house in neighborhood B, what is the portfolio risk of your investment?

SCENARIO 16-16 Given below are the average prices for three types of energy products for five consecutive years. Year Electricity Natural Gas Fuel Oil 1 43.205 25.893 0.892 2 16.959 28.749 0.969 3 47.202 28.933 1.034 4 48.874 29.872 0.913 5 48.693 28.384 0.983 -Referring to Scenario 16-16, what are the simple price indices for electricity, natural gas and fuel oil, respectively, in year 3 using year 5 as the base year?

SCENARIO 8-16 A random sample of 100 stores from a large chain of 500 garden supply stores was selected to determine the mean number of lawnmowers sold at an end-of-season clearance sale. The sample results indicated a mean of 6 and a standard deviation of 2 lawnmowers sold. A 95% confidence interval (5.623 to 6.377) was established based on these results. -Referring to Scenario 8-16, if the population had consisted of 1,000 stores, the confidence interval estimate of the mean with finite population correction would have been wider in range.

SCENARIO 4-17 Jake woke up late in the morning on the day that he has to go to school to take an important test. He can either take the shuttle bus which is usually running late 20% of the time or ride his unreliable motorcycle which breaks down 40% of the time. He decides to toss a fair coin to make his choice. -Referring to Scenario 4-17, if Jake, in fact, gets to the test on time, what is the probability that he rode his bike?

SCENARIO 11-12 A student team in a business statistics course designed an experiment to investigate whether the brand of bubblegum used affected the size of bubbles they could blow. To reduce the person-to-person variability, the students decided to use a randomized block design using themselves as blocks. Four brands of bubblegum were tested. A student chewed two pieces of a brand of gum and then blew a bubble, attempting to make it as big as possible. Another student measured the diameter of the bubble at its biggest point. The following table gives the diameters of the bubbles (in inches) for the 16 observations. -Referring to Scenario 11-12, the decision made at a 0.05 level of significance on the F test for the block effects implies that the blocking has been advantageous in reducing the experiment error.

SCENARIO 16-17 Given below are the prices of a basket of four food items from 2008 to 2012. Year Wheat( \/ Bushel) Corn( \/ Bushel) Soybeans( \/ Bushel) Milk( \/ hundredweight) 2008 4.25 3.71 7.41 15.03 2009 3.43 2.7 7.55 13.63 2010 2.63 2.3 6.05 15.18 2011 2.11 1.97 4.68 14.72 2012 2.16 1.9 4.81 12.32 -Referring to Scenario 16-17, what are the simple price indices for wheat, corn, soybeans and milk, respectively, in 2008 using 2012 as the base year?

SCENARIO 4-17 Jake woke up late in the morning on the day that he has to go to school to take an important test. He can either take the shuttle bus which is usually running late 20% of the time or ride his unreliable motorcycle which breaks down 40% of the time. He decides to toss a fair coin to make his choice. -Referring to Scenario 4-17, if Jake, in fact, gets to the test on time, what is the probability that he took the bus?