A defective car has a probability of 2/3 upon turning on the ignition in each attempt. Assume attempts

are independent.

• (a) What is the probability that exactly 3 attempts are needed until the car starts?

• (b) What is the probability that 3 or 4 attempts are needed?

• (c) What is the probability of success in 4 or more trials?

Simulate the effect of the Price change if it will follow the following pattern for Type A. (build the 95% confidence interval) Type A (Price (million Dollar) =1.25 (20% probability); Price (million Dollar) =2.25 (40 % probability); Price (million Dollar) =3 (25 % probability); Price (million Dollar) =3.5 (15 % probability))

Match the terms with the following descriptions:
population sample population size sample size population mean sample mean variance standard deviation alpha null hypothesis alternative hypothesis degrees of freedom hypothesized mean p-value t-statistic

The set of data for ALL individuals or items of interest., e.g. everyone in the world, the entire of Texas, all of our customers, etc. __________
Data you take randomly from the population because it’s too costly or not feasible to measure the entire population. A subset of the population. __________
The count of ALL the objects, people, or things in the entire population.__________
The total number or count of ALL individuals or items of interest in the dataset in a subset of the population.__________
The true average of the entire population, which is rarely known. However, the sample mean can be used as a close substitute for that of the entire population’s. The symbol for this term is useful when writing the null and alternative hypotheses to remind us why we use statistics: to infer about the population from random samples. __________
The average of all values in a subset of the population. It is calculated by taking the sum of all values in a sample and dividing by the sample size and can be used as an estimate of the population mean.__________
A measure of dispersion around the mean equal to the positive square root of the variance. It tells us how large a difference from the mean can be expected in the data. A low number indicates that most of the data are near the mean. A high number means that the data is spread out.__________
A measure of dispersion around the mean. It is the average of the squared distances between an observation and the mean. A high number indicates the data is spread out across a wide range of values. A Low number indicates the data is bunched around the mean value. __________
The level of significance needed to reject the null hypothesis. It is the maximum allowable probability of false negative, where the null hypothesis is rejected when it is in fact true. This value is set by the investigator of the hypotheses. For example, if you want to be 95% confident in your statistical conclusions, you have a level of significance of 5%. __________
A speculated value for the population average used in the null hypothesis. In a one-sample t-test this is the benchmark value that the sample mean is compared against. __________
The default hypothesis to be tested. This hypothesis is rejected when the p-value is below the desired level of significance. __________
If the null hypothesis is rejected, this other hypothesis is confirmed. For example, in the legal principle “innocent until proven guilty”, innocent is the null hypothesis and guilty is this other hypothesis. __________
The observed level of significance for a test statistic. Assuming the null hypothesis is true, it is the probability of observing a test statistic equal to or larger than the one obtained from the sample. This value is what is returned by the T.DIST.2T or T.TEST function in Excel. __________
The number of observations minus the number of statistics needed to estimate a population parameter. For example, the sample variance is an estimate of the population variance and requires one statistic, the sample mean, to be calculated. This number is used in calculating the t-statistic and thereby the p-value. __________
A standardized measure of the distance between two means. It is the ratio of the difference between two means and their standard error. It is an input for the calculation of the p-value, which determines significance.__________

The following information provides details of the cost, volume and cost drivers for the particular period in respect of ABC & Co. Products X Y Z Total Production and sales (units) 30,000 20,000 8,000 Raw material usage (units) 5 5 11 Direct material cost GHS 25 GHS 20 GHS 11 GHS 1,238,000 Direct labour hours 1⅓ 2 1 88,000 Machine hours 1⅓ 1 2 76,000 Direct labour cost 8 12 6 Number of production run 3 7 20 30 Number of deliveries 9 3 20 32 Number of receipts 15 35 220 270 Number of production orders 15 10 25 50 Overhead Cost: GHS Set-up 30,000 Machines 760,000 Receiving 435,000 Packing 250,000 Engineering 373,000 1,848,000 In the past the company has allocated overhead to products on the basis of direct labour hours. However, the majority of overheads are more closely related to machine hours than direct labour hours. The company has recently redesigned its cost system by recovering overheads using two volume-related bases: machine hours and material handling overhead rate for recovering overheads of the receiving department. Both the current and previous cost system reported low profit margin for product X, which is the company’s highest selling product. The management accountant has recently attended a conference on activity-based costing and the overhead cost for the last period have been analysed by major activities in order to compute activity-based costs. Required: 3 (a) Compute the product cost using a traditional volume-related costing system based on the assumptions that: i. All overheads are recovered on the basis of direct labour hours ii. The overheads of the receiving department are recovered by a material handling overhead rate and the remaining overheads are recovered using a machine hour rate. (b) Compute product costs using an activity-based costing system.

The students in one college have the following rating system for their professors:excellent, good, fair, and bad. In a recent poll of the students, it was found that they believe that 20% of the professors are excellent, 50% are good, 20% are fair, and 10% are bad. Assume that 12 professors are randomly selected from the college.
a. What is the probability that 6 are excellent, 4 are good, 1 is fair, and 1 is bad?
b. What is the probability that 6 are excellent, 4 are good, and 2 are fair?
c. What is the probability that 6 are excellent and 6 are good?
d. What is the probability that 4 are excellent and 3 are good?
e. What is the probability that 4 are bad?
f. What is the probability that none is bad?

An urn contains 5 red balls and 5 blue balls.

​(a) If 3 balls are selected all at​ once, what is the probability that 2 are blue and 1 is​ red?

​(b) If 3 balls are selected by pulling out a​ ball, noting its​ color, and putting it back in the urn before the next​ section, what is the probability that only the first and third balls drawn are​ blue? ​

(c) If 3 balls are selected one at a time without putting them back in the​ urn, what is the probability that only the first and third balls are​ blue? ​

(a) The probability that 2 balls are blue and 1 is red is__? ​

(b) The probability is __? ​

(c) The probability is __? ​

Sixty percent of dogs from a certain breed will chase a thrown ball. In a group of 15 dogs of this breed,

What’s the probability that less than 10 will chase a ball?

What’s the probability that at least 12 will chase a ball?

What’s the probability that exactly 8 will chase a ball?

What’s the probability that at most 4 will not chase a ball?

Glenn Foreman, president of Oceanview Development Corporation, is considering submit- ting a bid to purchase property that will be sold by sealed bid at a county tax foreclosure. Glenn’s initial judgment is to submit a bid of $5 million. Based on his experience, Glenn estimates that a bid of $5 million will have a 0.2 probability of being the highest bid and securing the property for Oceanview. The current date is June 1. Sealed bids for the prop- erty must be submitted by August 15. The winning bid will be announced on September 1.
If Oceanview submits the highest bid and obtains the property, the firm plans to build and sell a complex of luxury condominiums. However, a complicating factor is that the property is currently zoned for single-family residences only. Glenn believes that a ref- erendum could be placed on the voting ballot in time for the November election. Passage of the referendum would change the zoning of the property and permit construction of the condominiums.
The sealed-bid procedure requires the bid to be submitted with a certified check for 10% of the amount bid. If the bid is rejected, the deposit is refunded. If the bid is accepted, the deposit is the down payment for the property. However, if the bid is accepted and the bidder does not follow through with the purchase and meet the remainder of the financial obligation within six months, the deposit will be forfeited. In this case, the county will offer the property to the next highest bidder.
To determine whether Oceanview should submit the $5 million bid, Glenn conducted some preliminary analysis. This preliminary work provided an assessment of 0.3 for the prob- ability that the referendum for a zoning change will be approved and resulted in the following estimates of the costs and revenues that will be incurred if the condominiums are built:
If Oceanview obtains the property and the zoning change is rejected in November, Glenn believes that the best option would be for the firm not to complete the purchase of the property. In this case, Oceanview would forfeit the 10% deposit that accompanied the bid.
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Cost and revenue Estimates
Revenue from condominium sales
Cost Property Construction expenses
$15,000,000
$5,000,000

$8,000,000

Because the likelihood that the zoning referendum will be approved is such an impor- tant factor in the decision process, Glenn suggested that the firm hire a market research service to conduct a survey of voters. The survey would provide a better estimate of the likelihood that the referendum for a zoning change would be approved. The market re- search firm that Oceanview Development has worked with in the past has agreed to do the study for $15,000. The results of the study will be available August 1, so that Oceanview will have this information before the August 15 bid deadline. The results of the survey will be either a prediction that the zoning change will be approved or a prediction that the zoning change will be rejected. After considering the record of the market research service in previous studies conducted for Oceanview, Glenn developed the following probability estimates concerning the accuracy of the market research information:
where
P(A Z s1) 5 0.9   P(N Z s1) 5 0.1 P(A Z s2) 5 0.2   P(N Z s2) 5 0.8
A 5 prediction of zoning change approval N 5 prediction that zoning change will not be approved s1 5 the zoning change is approved by the voters s2 5 the zoning change is rejected by the voters
managerial report
Perform an analysis of the problem facing the Oceanview Development Corporation, and prepare a report that summarizes your findings and recommendations. Include the follow- ing items in your report:
1.   A decision tree that shows the logical sequence of the decision problem 2. A recommendation regarding what Oceanview should do if the market research
information is not available 3.   A decision strategy that Oceanview should follow if the market research is conducted 4. A recommendation as to whether Oceanview should employ the market research
firm, along with the value of the information provided by the market research firm Include the details of your analysis as an appendix to your report.

The downtime per day for a computing facility has mean 4 hours and standard deviation 0.9 hour. (a) Suppose that we want to compute probabilities about the average daily downtime for a period of 30 days. (i) What assumptions must be true to use the result of the central limit theorem to obtain a valid approximation for probabilities about the average daily downtime? (Select all that apply.) The daily downtimes must have an approximately normal distribution. The number of daily downtimes must be greater than 30. The daily downtimes must have an expected value greater than their variance. The daily downtimes must have the same expected value and variance. The daily downtimes must be independent and identically distributed random variables. (ii) Under the assumptions described in part (i), what is the approximate probability that the average daily downtime for a period of 30 days is between 1 and 5 hours? (Round your answer to four decimal places.) (b) Under the assumptions described in part (a), what is the approximate probability that the total downtime for a period of 30 days is less than 119 hours? (Round your answer to four decimal places.)