1. You have sampled 25 randomly selected students to find the mean test score. A 95% confidence interval for the mean came out to be between 85 and 92. Which of the following statements gives a valid interpretation of this interval?
1)If this procedure were to be repeated many times, 95% of the confidence intervals found would contain the true mean score.
2)If 100 samples were taken and a 95% confidence interval were found, 95 of them would be between 85 and 92
3)95% of the 25 students have a mean between 85 and 92

2. As standard deviation increases, samples size _____________ to achieve a specified level of confidence.
1) Increases 2)Decreases 3) No answer text provided.

3. In a manufacturing process a random sample of 9 bolts manufactured has a mean length of 3 inches with a standard deviation of 0.3. What is the 90% confidence interval for the true mean length of the bolt?
1) 2.8355 to 3.1645
2) 2.4420 to 3.5580
3) 2.814 to 3.1859

1. The following table contains the demand from the last 5 months.

1. Calculate the single exponential smoothing forecast for these data using an α of 0.3 and an initial forecast (F₁) of 28. Report the forecast for Month 6 in AnswerSheet. Show your work in worksheet “Show your work for Q1.” (2 pts.)

2. Calculate the exponential smoothing with trend forecast for these data using an α of 0.25, a β of 0.60, an initial trend forecast (T₁) of 1, and an initial exponentially smoothed forecast (F₁) of 28. Report the forecast including trend (FIT) for Month 6 in AnswerSheet. Show your work in worksheet “Show your work for Q1.” (2 pts.)

3. Calculate the mean absolute deviation (MAD) for each forecast. Which forecasting method performs better in this problem (pick from the list)? Show your work in worksheet “Show your work for Q1.” (3 pts.)

1-A contractor decided to build homes that will include the middle 80% of the market. If the average size of homes built is 1750 square feet, find the maximum and minimum sizes of the homes the contractor should build. Assume that the standard deviation is 96 square feet and the variable is normally distributed.

2-Determine the indicated probability for a binomial experiment with the given number of trials n and the given success probability p. n = 13, p = 0.7, P(Fewer than 4)

3-A student takes a 5 question multiple choice quiz with 4 choices for each question. If the student guesses at random on each question, what is the probability that the student gets exactly 2 questions correct?

4- An investor is considering a $15,000 investment in a start-up company. She estimates that she has probability 0.15 of a $10,000 loss, probability 0.1 of a $10,000 profit, probability 0.3 of a $30,000 profit, and probability 0.45 of breaking even (a profit of $0). What is the expected value of the profit? $11,500 $15,250 $10,000 $8,500

50-1/1

Assuming competitive markets with typical supply and demand curves, which of the following statements is correct?

• An increase in demand with no change in supply will result in an increase in sales.

• An increase in supply with no change in demand will result in an increase in price.

• An increase in supply with a decrease in demand will result in an increase in price.

• An increase in supply with no change in demand will result in a decline in sales.

53.1/1

Refer to the given consumption schedules. DI signifies disposable income and C represents consumption expenditures. All figures are in billions of dollars. The marginal propensity to consume in economy (1) is

• 0.7.

• 0.5.

• 0.3.

• 0.8.

An oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the following prior probabilities:

P(high-quality oil) = .3

P(medium-quality oil) =.5

P(no oil) = .2

a. What is the probability of finding oil (to 1 decimal)? ______

b. After 200 feet of drilling on the first well, a soil test is taken. The probabilities of finding the particular type of soil identified by the test are given below:

P(soil/high-quality oil) = 0.3

P(soil/medium-quality oil) = 0.5

P(soil/no oil) = 0.2

Given the soil found in the test, use Bayes' theorem to compute the following revised probabilities (to 4 decimals).

P(high-quality oil/soil) = _____

P(medium-quality oil/soil) = _____

P(no oil/soil) = ______

What is the new probability of finding oil (to 4 decimals)? _____

According to the revised probabilities, what is the quality of oil that is most likely to be found?

^High quality, medium quality, or no oil?

1. (a) If A and B are independent events with P(A) = 0.6 and P(B) = 0.7, find P (A or B).

(b) A randomly selected student takes Biology or Math with probability 0.8, takes Biology and Math with probability 0.3, and takes Biology with probability 0.5. Find the probability of taking Math.

2. A box contains 4 blue, 6 red and 8 green chips.

1. In how many different ways can you select 2 blue, 3 red and 5 green chips? (Give the exact numerical value).

2. Draw two chips in a row without replacement. Find the probability that both chips are green.

3. Based on the following table, compute the probabilities below:

P (Women and Yes) =

P (Men | Yes) =

P (No | Women) =

P (Men or No) =

Are Men and No Opinion mutually exclusive?

Are Men and No Opinion independent? Justify your answer by an appropriate computation.

1. A researcher wanted to estimate the mean contributions made to charitable causes by all major companies. A random sample of 18 companies produced by the following data on contributions (in millions of dollars) made by them.
1.8, 0.6, 1.2, 0.3, 2.6, 1.9, 3.4, 2.6, 0.2
2.4, 1.4, 2.5, 3.1, 0.9, 1.2, 2.0, 0.8, 1.1

Assume that the contributions made to charitable causes by all major companies have a normal distribution.
a. What is the point estimate for the population mean?
b. Construct a 98% confidence interval for the population mean.
c. What sample size would the researcher need to obtain a margin of error of 100,000 for the same confidence level? (Assume that the sample standard deviation obtained from his original sample is equal to the population standard deviation.)
d. Prior to collecting the data, the researcher believed that the mean contribution of all companies was less than $2.5 million. For a significance level of 0.01, test the researchers hypothesis.

A facility has a waste storage tank with a capacity of 40 cubic feet. Each week the tank produces either 0, 10, 20, or 30 cubic feet of waste with respective probabilities of 0.1, 0.4, 0.3, and 0.2. If the amount of waste produced in a week creates a situation where the tank would overflow, the amount exceeding the tank’s capacity can be removed at a cost of $3 per cubic foot. At the end of each week, a contracted service is available to remove waste. The service costs $40 for each visit plus $1 per cubic foot of waste removed. The facility manager decides to adopt a policy where, if the tank contains more than 20 cubic feet of waste, the contract service comes at the end of the week and removes all of the waste in the tank. Otherwise, the service does not come, and no waste is removed. Model the amount of waste in the tank as a Markov chain. Pay particular attention to when (at what point in the week) the amount of waste is measured or recorded

1) The daily demand, D, of sodas in the break room is:

i) Find the probability that the demand is at most 2.
ii) Compute the average demand of sodas.
iii) Compute SD of daily demand of sodas.

2) From experience you know that 83% of the desks in the schools have gum stuck
beneath them. In a random sample of 14 desks.
a) Compute the probability that all of them have gum underneath.
b) Compute the probability that 10 or less desks have gum.
c) What is the probability that more than 10 have gum?
d) What is the expected number of desks in the sample have gum?
e) What is the SD of the number of desks with gum?

3) The number of customers, X, arriving in a ATM in the afternoon can be modeled
using a Poisson distribution with mean 6.5.
a) Compute P(X<3).
b) Compute P(X>4).
c) SD of X.

A 4.5m4.5m foundation carries a load of 3000 kN. The foundation rests at a depth of 1.5m
below the ground surface. The bearing soil is an extended sand with a saturated unit weight
(γsat) of 19 kN/m3
, modulus of elasticity (E) of 35 MPa, and Poisson’s ratio (µ) of 0.3. The
water level coincides with the ground surface.
a) Determine the effective vertical stresses (σ̍v) for points underneath the corner and
center of the foundation and located at a depth of 6.0 m from the ground surface.
Note: for estimating Δσ̍v (i.e., the additional vertical stresses), use both of the
influence coefficient and approximate methods. Comment on your results.
b) If we consider this foundation as a rigid element, what would be its uniform
settlement under the given load? Is it safe (and why)?
c) Calculate the time-dependent maximum, minimum, and differential settlements of the
foundation if sand is interrupted by a 2m-thick clay layer that starts at a depth of 5m
below the ground surface. Is it safe (and why)?
Note: For the clay, take Cc = 0.2 and e = 0.7.