The table below shows the number of male and female students enrolled in nursing at a particular university for a recent semester.
(a) Find the probability that a randomly selected student is male, given that the student is a nursing major
(b) Find the probability that a randomly selected student is a nursing major, given that the student is male.
Nursing Majors  Nonnursing majors  Total  
Males  97  1082  1179 
Females  750  1633  2383 
Total  847  2715  3562 
(a) Find the probability that a randomly selected student is male, given that the student is a nursing major
The probability is _______ .
(Round to three decimal places as needed.)
In: Math
The Westchester Chamber of Commerce periodically sponsors public service seminars and programs. Currently, promotional plans are under way for this year's program. Advertising alternatives include television, radio, and online. Audience estimates, costs, and maximum media usage limitations are as shown: Constraint Television Radio Online Audience per advertisement 110,000 18,000 30,000 Cost per advertisement $1,500 $250 $500 Maximum media usage 11 21 13 To ensure a balanced use of advertising media, radio advertisements must not exceed 50% of the total number of advertisements authorized. In addition, television should account for at least 10% of the total number of advertisements authorized.
(a) If the promotional budget is limited to $23,000, how many commercial messages should be run on each medium to maximize total audience contact? If your answer is zero enter “0”. Advertisement Alternatives No of commercial messages Television Radio Online What is the allocation of the budget among the three media? Advertisement Alternatives Budget ($) Television $ Radio $ Online $ What is the total audience reached?
(b) By how much would audience contact increase if an extra $100 were allocated to the promotional budget? Round your answer to the nearest whole number. Increase in audience coverage of approximately
In: Math
Assume that the helium porosity (in percentage) of coal samples taken from any particular seam is normally distributed with true standard deviation 0.74.
(a) Compute a 95% CI for the true average porosity of a certain seam if the average porosity for 20 specimens from the seam was 4.85.
(b) Compute a 98% CI for true average porosity of another seam based on 13 specimens with a sample average porosity of 4.56.
(c) How large a sample size is necessary if the width of the 95% interval is to be 0.4?
(d) What sample size is necessary to estimate true average porosity to within 0.21 with 99% confidence?
In: Math
1. Which of the following is not a characteristic of the normal probability distribution?
a. 
The distribution is symmetrical 

b. 
The mean of the distribution can be negative, zero, or positive 

c. 
The standard deviation must be 1 

d. 
The mean, median, and the mode are equal 
2. If , n = 12, and the slope equals 0.5, then the yintercept of the least squares line is b_{0} = 276.08.
True
False
3. The coefficient of correlation r is a number that indicates the direction and the strength of the linear relationship between the dependent variable y and the independent variable x.
True
False
4. The function that defines the probability distribution of a continuous random variable is a
a. 
uniform function. 

b. 
normal function. 

c. 
either normal of uniform depending on the situation. 

d. 
probability density function. 
In: Math
It is common in many industrial areas to use a filling machine to fill boxes full of product. This occurs in the food industry as well as other areas in which the product is used in the home, for example, detergent. These machines are not perfect, and indeed they may A, fill to specification, B, underfill, and C, overfill. Generally the practice of underfilling is that which one hopes to avoid. Let P(C) = 0.034 while P(A) = 0.960.
(a) What is the probability that the box is underfilled, P(B)?
(b) What is the probability that the machine does not overfill?
(c) What is the probability that the machine either overfills or underfills?
In: Math
Your manager is trying to determine what forecasting method to use. Based upon the following historical data, calculate the following forecast and specify what procedure you would utilize.
MONTH  ACTUAL DEMAND  
1  59  
2  62  
3  64  
4  65  
5  73  
6  75  
7  75  
8  78  
9  78  
10  81  
11  82  
12  85  
a. Calculate the simple threemonth moving average forecast for periods 4–12. (Round your answers to 3 decimal places.)
Month  ThreeMonth Moving Average 

4  
5  
6  
7  
8  
9  
10  
11  
12  
b. Calculate the weighted threemonth moving average for periods 4–12 using weights of 0.40 (for the period t−1); 0.50 (for the period t−2), and 0.10 (for the period t−3). (Do not round intermediate calculations. Round your answers to 1 decimal place.)
Month  ThreeMonth Weighted Moving Average 

4  
5  
6  
7  
8  
9  
10  
11  
12  
c. Calculate the single exponential smoothing forecast for periods 2–12 using an initial forecast (F_{1}) of 58 and an α of 0.40. (Do not round intermediate calculations. Round your answers to 3 decimal places.)
Month  Single Exponential Smoothing Forecast 

2  
3  
4  
5  
6  
7  
8  
9  
10  
11  
12  
d. Calculate the exponential smoothing with trend component forecast for periods 2–12 using an initial trend forecast (T_{1}) of 1.50, an initial exponential smoothing forecast (F_{1}) of 57, an α of 0.40, and a δ of 0.40. (Do not round intermediate calculations. Round your answers to 3 decimal places.)
Month  Exponential Smoothing with Trend 

2  
3  
4  
5  
6  
7  
8  
9  
10  
11  
12  
e1. Calculate the mean absolute deviation (MAD) for the forecasts made by each technique in periods 4–12. (Do not round intermediate calculations. Round your answers to 3 decimal places.)
Mean Absolute Deviation 

Threemonth moving average  
Threemonth weighted moving average  
Single exponential smoothing forecast  
Exponential smoothing with trend  
e2. Which forecasting method is best?
Single exponential smoothing forecast  
Threemonth weighted moving average  
Threemonth moving average  
Exponential smoothing with trend forecast 
In: Math
A data set includes data from student evaluations of courses. The summary statistics are n=93, x overbar equals=4.08 sequals=0.65. Use a 0.10 significance level to test the claim that the population of student course evaluations has a mean equal to 4.25
Assume that a simple random sample has been selected. Identify the null and alternative hypotheses, test statistic, Pvalue, and state the final conclusion that addresses the original claim.
In: Math
Seth Bullock, the owner of Bullock Gold Mining, is evaluating a new gold mine in South Dakota. Dan Dority, the company’s geologist, has just finished his analysis of the mine site. He has estimated that the mine would be productive for eight years, after which the gold would be completely mined. Dan has taken an estimate of the gold deposits to Alma Garrett, the company’s financial officer. Alma has been asked by Seth to perform an analysis of the new mine and present her recommendation on whether the company should open the new mine. Alma has used the estimates provided by Dan to determine the revenues that could be expected from the mine. She has also projected the expense of opening the mine and the annual operating expenses. If the company opens the mine, it will cost $635 million today, and it will have a cash outflow of $45 million nine years from today in costs associated with closing the mine and reclaiming the area surrounding it. The expected cash flows each year from the mine are shown in the table. Bullock Mining has a required return of 12 percent on all of its gold mines.
Year 
Cash Flow 
0 1 2 3 4 5 6 7 8 9 
−$635,000,000 89,000,000 105,000,000 130,000,000 173,000,000 205,000,000 155,000,000 145,000,000 122,000,000 − 45,000,000 
Construct a spreadsheet to calculate the payback period, internal rate of return, modified internal rate of return, and net present value of the proposed mine.
Based on your analysis, should the company open the mine?
In: Math
Find the standard deviation, s, of sample data summarized in the frequency distribution table below by using the formula below, where x represents the class midpoint, f represents the class frequency, and n represents the total number of sample values. Also, compare the computed standard deviation to the standard deviation obtained from the original list of data values, 11.1
\(S=\sqrt{\frac{n\left[\sum\left(1 \cdot x^{2}\right)\right]\left[\sum(t+x)\right]^{2}}{n(n1)}}\)
Interval  30.36  3743  44.50  5157  53.84  6571  72.78 

Frequency  2  2  1  1  13  28  30 
Standard deviations=
(Round to one decimal place as needed.)
Consider a difference of 20% between two values of a standard deviation to be significant. How does this computer values compare with the given standard deviation 11.1?
the computer values is not significantly different from the given value
the computer values is significantly greater than the given value
the computer values is significantly less than the given values
In: Math
Find the indicated IQ score. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.
The indicated IQ score, x, is _______ (Round to one decimal place as needed.)
Find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1.
The area of the shaded region is _______ (Round to four decimal places as needed.)
Find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1.
The area of the shaded region is _______ (Round to four decimal places as needed.)
In: Math
A group of students estimated the length of one minute without reference to a watch or clock, and the times (seconds) are listed below. Use a 0.10 significance level to test the claim that these times are from a population with a mean equal to 60 seconds. Does it appear that students are reasonably good at estimating one minute?
71 79 39 63 41 27 59 66 68 46 66 72 91 87 63
What are the null and alternative hypotheses?
In: Math
There are two traffic lights on a commuter's route to and from work. Let X_{1} be the number of lights at which the commuter must stop on his way to work, and X_{2} be the number of lights at which he must stop when returning from work. Suppose that these two variables are independent, each with the pmf given in the accompanying table (so X_{1}, X_{2} is a random sample of size n = 2).
x_{1}  0  1  2  μ = 1, σ^{2} = 0.6  
p(x_{1})  0.3  0.4  0.3 
(a) Determine the pmf of T_{o} = X_{1} + X_{2}.
t_{o}  0  1  2  3  4 
p(t_{o}) 
(b) Calculate
μ_{To}.
μ_{To}
=
How does it relate to μ, the population mean?
μ_{To} = ·
μ
(c) Calculate
σ_{To}^{2}.
σ_{To}^{2}  = 
How does it relate to σ^{2}, the population
variance?
σ_{To}^{2}
= · σ^{2}
(d) Let X_{3} and X_{4} be the
number of lights at which a stop is required when driving to and
from work on a second day assumed independent of the first day.
With T_{o} = the sum of all four
X_{i}'s, what now are the values of
E(T_{o}) and
V(T_{o})?
E(T_{o}) =  
V(T_{o}) = 
(e) Referring back to (d), what are the values of
P(T_{o} = 8) and P(T_{o} ≥ 7)
[Hint: Don't even think of listing all possible outcomes!] (Enter your answers to four decimal places.)
P(T_{o} = 8) = 

P(T_{o} ≥ 7) = 
There are two traffic lights on a commuter's route to and from work. Let X_{1} be the number of lights at which the commuter must stop on his way to work, and X_{2} be the number of lights at which he must stop when returning from work. Suppose that these two variables are independent, each with the pmf given in the accompanying table (so X_{1}, X_{2} is a random sample of size n = 2).
(a) Determine the pmf of T_{o} = X_{1} + X_{2}.
P(T_{o} = 8) and P(T_{o} ≥ 7) [Hint: Don't even think of listing all possible outcomes!] (Enter your answers to four decimal places.)

In: Math
A random sample of 40 students has a mean annual earnings of $3120.
Assume the population standard deviation, σ, is $677. (Section 6.1)
• Construct a 95% confidence interval for the population mean annual earnings of students.
Margin of error, E._______ Confidence interval: _______ <μ< _______
• If the number of students sampled was reduced to 25 and the level of confidence remained at 95%, what would be the new error margin and confidence interval?
Margin of error, E._______ Confidence interval: _______ <μ< _______
• Did the confidence interval increase or decrease and why?
• If the number of students sampled was increased to 100 and the level of confidence remained at 95%, what would be the new confidence interval?
Margin of error, E._______ Confidence interval: _______ <μ< _______
• Did the confidence interval increase or decrease and why?
In: Math
Silicone implant augmentation rhinoplasty is used to correct congenital nose deformities. The success of the procedure depends on various biomechanical properties of the human nasal periosteum and fascia. An article reported that for a sample of 20 (newly deceased) adults, the mean failure strain% was 26.0, and the standard deviation was 3.5.
(a) Assuming a normal distribution or failure strain, estimate true average strain in a way that conveys information about precision and reliability. confidence interval. Round your answers to two decimal places.)
(b) Predict the strain for a single adult in a way that conveys information about precision and reliability. (Use a 95% prediction interval. Round your answers to two decimal places.)
How does the prediction compare to the estimate calculated in part (a)?
The prediction interval is much wider than the confidence interval in part (a)
The prediction interval is much narrower than the confidence interval in part (a)
The prediction interval is the same as the confidence interval in part (a)
In: Math