In a survey of​ four-year colleges and​ universities, it was found that 255 offered a liberal arts degree. 110 offered a computer engineering degree. 481 offered a nursing degree. 30 offered a liberal arts degree and a computer engineering degree. 211 offered a liberal arts degree and a nursing degree. 86 offered a computer engineering degree and a nursing degree. 25 offered a liberal arts​ degree, a computer engineering​ degree, and a nursing degree. 33 offered none of these degrees.

A.  How many​ four-year colleges and universities were​surveyed? There were ___​four-year colleges and universities surveyed. Of the​ four-year colleges and universities​ surveyed, how many offered

B.  a liberal arts degree and a nursing​ degree, but not a computer engineering ​degree? There are ____ ​four-year colleges and universities that offer a liberal arts degree and a nursing​degree, but not a computer engineering degree.

C.  a computer engineering ​degree, but neither a liberal arts degree nor a nursing​ degree? There are ____ ​four-year colleges and universities that offer a computer engineering ​degree, but neither a liberal arts degree nor a nursing degree.

D.  a liberal arts​ degree, a computer engineering​ degree, and a nursing​ degree? There are ____ ​four-year colleges and universities that offer a liberal arts​ degree, a computer engineering​ degree, and a nursing degree. Enter your answer in each of the answer boxes.

among the thirty largest us cities, the mean one-way commute time to work is 25.8 minutes. the longest one-way travel time is in new york city, where the mean is 37.7 minutes. assume the distribution of travel time in new york city follows the normal probability distribution and the standard deviation is 6.7 minutes.

A. What percent of the New York City commutes are for less than 27 minutes? (Round your intermediate calculations and final answer to 2 decimal places)

B. What percent are between 27 and 33 minutes?  (Round your intermediate calculations and final answer to 2 decimal places)

C. What percent are between 27 and 47 minutes?  (Round your intermediate calculations and final answer to 2 decimal places)

A die is weighted so that rolling a 1 is two times as likely as rolling a 2, a 2 is two times likely as rolling a 3, a 3 is two times as likely as rolling a 4, a 4 is two times a likely as rolling a 5, and a 5 is two times as likely as rolling a 6. What is the probability of rolling an even number?

1. To benchmark their performance against competing healthcare institutions, a radiology center wants to know the average time taken by their staff to do an MRI test. A sample of 50 randomly selected MRI tests yielded a sample average of 47 minutes and a sample standard deviation of 9 minutes. The distribution of testing time, however, is highly skewed to the right.

   1. Suggest a plausible reason for the distribution of the MRI testing time to be right skewed.

   2. Why can one still make an inference about the average MRI testing time even though the

      distribution is skewed right?

   3. Compute a 90% confidence interval for the average MRI testing time

suppose you want to determine the mean number of cans of soda drunk each month by students in their twenties at your school. Describe a possible sampling method in three to five complete sentences.

2M2_IND3. Prices of diamond jewelry are based on the “4Cs” ofdiamonds: cut, color, clarity, and carat. A jeweler is trying to estimate the price of diamond earrings based on color, carats, and clarity. The jeweler has collected some data on 22 diamond pieces and the data is shown in Worksheet IND3. The jeweler wouldlike to build a multiple regression model to estimate the price of the pieces based on color, carats, and clarity.a)Prepare a scatter plot showing the relationship betweenthe price and each of the independent variables.b)If the jeweler wanted to build a regression model using only one independent variable to predict price, which variable should be used?c)Why?d)How do you use the value of Significance F in the model with only one independent variable?e)If the jeweler wanted to build a regression model using twoindependent variables to predict price, which variable should be addedto the variable selected in the one independent variable model?f)Why?g)If the jeweler wanted to build a regression model using three independent variables to predict price, which variable should be addedto the variables selectedfor the two variable model?h)Why?i)Based on your best model, how should the jeweler price a diamond with a color of 2.75, a clarity of 3.00, and a weight of 0.85 carats?j)How do you use the value of Significance F in the multiple regression model?k)Does there appear to be any multicollinearity among the independent variables?l)How can you tell if you have multicollinearity?

An experiment consists of flipping a coin 5 times and noting the number of times that a heads is flipped. Find the sample space SS of this experiment.

A traffic inspector has counted the number of vehicles passing through a certain point in 100 successive 20 – minute time periods. The observations are listed below.

You are required to:

a) Present these data on a grouped frequency distribution with class width of 5 for each class starting with 5 to 9, 10 to 14 and so on.                                    [5 marks]

b) Determine the real class limits and hence show the data on a histogram. [5marks]

c) Estimate the (I) mean (ii) Mode and (iii) Median.        [4 + 6+6 = 10 marks]

d) Estimate the (I) Quartiles (ii) Quartile Deviation (iii) Sample variance (iv) Sample standard deviation.           [6 + 2 + 4 + 2 = 14 marks]

e) Find the (I) Coefficient of variation (ii) Coefficient of Skewness.               [3 + 3 = 6 marks]

1)A group of 110 students sat an aptitude test, their resulting scores are presented:

66
61
66
76
70
64
67
66
71
64
63
61
65
67
67
72
62
64
69
65
72
53
76
69
60
76
70
62
70
71
71
71
64
63
69
65
79
63
64
66
61
58
80
74
61
67
70
62
71
69
79
75
73
72
66
68
72
72
67
63
76
61
75
64
84
73
53
76
71
65
64
61
74
74
72
78
70
83
77
79
67
69
79
66
62
70
75
66
61
75
77
69
75
63
68
69
74
76
79
72
72
58
67
65
58
75
53
62
64
76

a)Calculate the mean and standard deviation for the sample. Give your answers to 2 decimal places.

sample mean = ?

sample standard deviation = ?

b)Find the proportion of scores that are within 1 standard deviation of the sample mean and also the proportion that are within 2 standard deviations of the sample mean. Use the unrounded values for the mean and standard deviation when doing this calculation. Give your answers as decimals to 2 decimal places.

Proportion of scores within 1 standard deviation of the mean = ?

Proportion of scores within 2 standard deviations of the mean = ?

c)Select the appropriate description for the data:

a)the data are APPROXIMATELY normal
b)the data are CLEARLY not normal

d)Calculate the standardized value for the sample value 75. Note that, for a value x within a sample that is approximately distributed as N(x,s), a standardized value can be calculated as z = (x - x) / s

standardized value (to 2 decimal places) for the sample value 75 = ?

e)Calculate the probability that a standard normal random variable Z takes a values less than the standardized value calculated in part d). Give your answer as a decimal to 4 decimal places.

Probability Z less than standardized value = ?

f)Find the proportion of values in the sample that are less than 75. Give you answer as a decimal to 2 decimal places.

Proportion of values less than 75 = ?

2)

A group of mutual funds earned varying annual rates of return in the last year. These rates of return are normally distributed with a mean of 6% and a standard deviation of 17%.

One mutual fund in this group managed to earn a rate of return that was double that of this group's average that year. This performance would put the fund in the top X% of those funds in that year.

Calculate X%. Give your answer to 1 decimal place.

X% = %

1. The manufacturer of a portable music player (PMP) has shown that the average life of the product is 72 months with a standard deviation of 12 months. The manufacturer is considering using a new parts supplier for th PMP's and want to test that the new hard drives will increase the life of the PMP. Before manufacturing the PMP's on a lareg scale, the manufactuer sampled 200 PMP's and found the average life to be 78 months. Test the hypothesis using alpha = .01 that the new hard drives will increase the life of the PMP's. Assume the standard deviation of the new PMP's is the same as the standard deviation of the older model.
2. A website developer has indicated to potential clients that for the sites he has developed visitors spend an average of 45 minutes per day on the sites. One of his potential clients conducted a survey of 20 visitors to several of his sites and found that the average time spent was 35 minutes with a standard deviation of 7 minutes. Determine if there is sufficient evidence to conclude that the average time spent on the sites is different from what he indicated. Conduct the test at the 0.05 level.
3. In both cases, in addition to testing the hypotheses using a critical value, also calculate the p value for the test statistic.

Assume that X is normally distributed with a mean of 15 and a standard deviation of 2. Determine the value for x that solves:

P(X>x) = 0.5.

P(X < 13).

P(13 < X < 17).

Anystate Auto Insurance Company took a random sample of 358 insurance claims paid out during a 1-year period. The average claim paid was $1530. Assume σ = $230.

Find a 0.90 confidence interval for the mean claim payment. (Round your answers to two decimal places.)

Find a 0.99 confidence interval for the mean claim payment. (Round your answers to two decimal places.)

1. Given the data below, calculate the mean, calculate the standard deviation and explain the significance of each in the context of the data.

Let x represent the dollar amount spent on supermarket impulse buying in a 10-minute (unplanned) shopping interval. Based on a certain article, the mean of the x distribution is about $39 and the estimated standard deviation is about $7.

(a) Consider a random sample of n = 60 customers, each of whom has 10 minutes of unplanned shopping time in a supermarket. From the central limit theorem, what can you say about the probability distribution of x, the average amount spent by these customers due to impulse buying? What are the mean and standard deviation of the x distribution?

The sampling distribution of x is approximately normal with mean μ_x = 39 and standard error σ_x = $0.90.The sampling distribution of x is approximately normal with mean μ_x = 39 and standard error σ_x = $7.    The sampling distribution of x is approximately normal with mean μ_x = 39 and standard error σ_x = $0.12.The sampling distribution of x is not normal.

Is it necessary to make any assumption about the x distribution? Explain your answer.

It is necessary to assume that x has a large distribution.It is not necessary to make any assumption about the x distribution because n is large.    It is not necessary to make any assumption about the x distribution because μ is large.It is necessary to assume that x has an approximately normal distribution.

(b) What is the probability that x is between $37 and $41? (Round your answer to four decimal places.)


(c) Let us assume that x has a distribution that is approximately normal. What is the probability that x is between $37 and $41? (Round your answer to four decimal places.)


(d) In part (b), we used x, the average amount spent, computed for 60 customers. In part (c), we used x, the amount spent by only one customer. The answers to parts (b) and (c) are very different. Why would this happen?

The standard deviation is larger for the x distribution than it is for the x distribution.The mean is larger for the x distribution than it is for the x distribution.    The x distribution is approximately normal while the x distribution is not normal.The standard deviation is smaller for the x distribution than it is for the x distribution.The sample size is smaller for the x distribution than it is for the x distribution.

In this example, x is a much more predictable or reliable statistic than x. Consider that almost all marketing strategies and sales pitches are designed for the average customer and not the individual customer. How does the central limit theorem tell us that the average customer is much more predictable than the individual customer?

The central limit theorem tells us that small sample sizes have small standard deviations on average. Thus, the average customer is more predictable than the individual customer.The central limit theorem tells us that the standard deviation of the sample mean is much smaller than the population standard deviation. Thus, the average customer is more predictable than the individual customer.