The taxi and takeoff time for commercial jets is a random variable x with a mean of 8.3 minutes and a standard deviation of 2.2 minutes. Assume that the distribution of taxi and takeoff times is approximately normal. You may assume that the jets are lined up on a runway so that one taxies and takes off immediately after the other, and that they take off one at a time on a given runway. (a) What is the probability that for 36 jets on a given runway, total taxi and takeoff time will be less than 320 minutes? (Round your answer to four decimal places.) (b) What is the probability that for 36 jets on a given runway, total taxi and takeoff time will be more than 275 minutes? (Round your answer to four decimal places.) (c) What is the probability that for 36 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes? (Round your answer to four decimal places.)

A random sample of 12 steel ingots was taken from a production line. The masses. in kilograms, of these ingots are given below.

24.8 30.8 28.1 24.8 27.4 22.1

24.7 27.3 27.5 27.8 23.9 23.2

Assuming that this sample came from an underlying normal population, investigate the claim that its mean exceeds 25.0kg

2. Show that the first derivative of the the moment generating function of the geometric evaluated at 0 gives you the mean.

3. Let X be distributed as a geometric with a probability of success of 0.10.

a. Give a truncated histogram (obviously you cannot put the whole sample space on the x-axis of the histogram) of this random variable.

b. Give F(x)

c. Find the probability it takes 10 or more trials to get the first success.

d. Here is a challenge. What is the probability that it takes an even number of trials to get the first success, i.e., P(X=2,4,6,8,...)

Multi-part questions: Packer Fan Tours is the official tour company for the Green Bay Packers of the NFL. One of the events in the package is to sponsor a reception the night before a game for fans that is attended by 5 of the players from the team. There are 53 players on the Green Bay Packers' roster of which 22 are starters. Assume that the 6 players attending the reception this week are chosen randomly. Determine the probability of the following occurring:

a. None of the players at the reception are starters.

b. All of the players at the reception are starters.

c. Two of the players at the reception are starters.

d. Four of the players at the reception are starters.

When one company (A) buys another company(B), some workers of company B are terminated. Terminated workers get severance pay. To be fair, company A fixes the severance payment to company B workers as equivalent to company A workers who were terminated in the last one year. A 36-year-old Mohammed, worked for company B for the last 10 years earning 32000 per year, was terminated with a severance pay of 5 weeks of salary. Bill smith complained that this is unfair that someone with the same credentials worked in company A received more. You are called in to settle the dispute. You are told that severance is determined by three factors; age, length of service with the company and the pay. You have randomly taken a sample of 40 employees of company A terminated last year. You recorded

Number of weeks of severance pay

Age of employee

Number of years with the company

Annual pay in 1000s

2. How much variance is not explained by the model? Test the validity of the models that X predict Y (provide hypotheses, decision, conclusion and conclusion in the business context)

1An agronomist was interested in finding out the amount of potassium in corn leaves, not including the stems, after four different fertilizers had been used in a field of corn

A. If 5 plots of corn were used per fertilizer in a completely randomized manner, show the layout of an experiment.

B. If in the 5 plots per fertilizer, 2 stalks of corn per plot were to be sampled from the experimental area, show the Anova table and state the assumptions necessary to test the effects of fertilizer.

C. Comment on this design (in part(B)) and analysis.

* part A, B & C please with as much detail as possible

What is the difference between the scales of measurement? Specifically Ordinal, Interval and Ratio scales of measurement because they are all very similar. Please provide good examples and explanation so I can understand the difference and not be confused when trying to determine/ solve for a variable.

Example:

Each voter was asked to rate their support for the current government on a scale from 0-100 (zero indicates no support whatsoever, while 100 indicates fully supporting the current government).

Voter support is the dependent variable but is it ordinal or interval scale of measurement?

A new thermostat has been engineered for the frozen food cases in large supermarkets. Both the old and new thermostats hold temperatures at an average of 25°F. However, it is hoped that the new thermostat might be more dependable in the sense that it will hold temperatures closer to 25°F. One frozen food case was equipped with the new thermostat, and a random sample of 26 temperature readings gave a sample variance of 4.4. Another similar frozen food case was equipped with the old thermostat, and a random sample of 19 temperature readings gave a sample variance of 12.8. Test the claim that the population variance of the new thermostat temperature readings is smaller than that for the old thermostat. Use a 5% level of significance. How could your test conclusion relate to the question regarding the dependability of the temperature readings? (Let population 1 refer to data from the old thermostat.) (a) What is the level of significance? State the null and alternate hypotheses. H0: σ12 = σ22; H1: σ12 ≠ σ22 H0: σ12 > σ22; H1: σ12 = σ22 H0: σ12 = σ22; H1: σ12 > σ22 H0: σ12 = σ22; H1: σ12 < σ22 (b) Find the value of the sample F statistic. (Round your answer to two decimal places.) What are the degrees of freedom? dfN = dfD = What assumptions are you making about the original distribution? The populations follow independent chi-square distributions. We have random samples from each population. The populations follow independent normal distributions. The populations follow dependent normal distributions. We have random samples from each population. The populations follow independent normal distributions. We have random samples from each population. (c) Find or estimate the P-value of the sample test statistic. (Round your answer to four decimal places.) p-value > 0.100 0.050 < p-value < 0.100 0.025 < p-value < 0.050 0.010 < p-value < 0.025 0.001 < p-value < 0.010 p-value < 0.001 (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. (e) Interpret your conclusion in the context of the application. Reject the null hypothesis, there is sufficient evidence that the population variance is smaller in the new thermostat temperature readings. Fail to reject the null hypothesis, there is insufficient evidence that the population variance is smaller in the new thermostat temperature readings. Reject the null hypothesis, there is insufficient evidence that the population variance is smaller in the new thermostat temperature readings. Fail to reject the null hypothesis, there is sufficient evidence that the population variance is smaller in the new thermostat temperature readings.

A test has an overall mean of 150 and a standard deviation of 8.50. The distribution of scores for each sub-set is often closely approximated by the normal curve. What percentage of students will score lower than 142 or better than 158?

1. The table below shows the data on temperature (℉) reached on a given day and the number of cans of soft drinks sold from a particular vending machine in front of a grocery store. Temperature 70 75 80 90 93 98 72 75 95 98 91 83 Quantity 30 31 40 52 57 59 33 38 45 53 62 45 a. Draw a scatterplot for the data. b. Compute the least squares regression line ?̂. c. Interpret the slope and y-intercept if appropriate. d. Compute the linear correlation coefficient ? between temperature and the number of soft drinks sold. Does a linear relation exist between temperature and the number of soft drinks sold? e. How many cans of soft drinks can be sold at a temperature of 62℉? Round your answer to the nearest can.

Suppose you have been building a model using the k-means clustering algorithm and you keep finding that a certain variable is essentially ignored by the model (in other words, the variable is very similarly distributed across all clusters). Describe a method that can be used to exaggerate or minimize the impact of a variable when using k-means clustering. Why does this method work?

no additional info available, predictive analysis

A $1 coin is tossed until a head appears, and let N be the total number of times that the $1 coin is tossed. A $5 coin is then tossed N times. Let X count the number of heads appearing on the tosses of the $5 coin. Determine P(X = 0) and P(X = 1).

An engineer is studying the effect of cutting speed on the rate of metal removal in a machining operation. However, the rate of metal removal is also related to the hardness of the test specimen. Five observations are taken at each cutting speed. The amount of metal removed y and the hardness of the specimen x are shown below in the format of a data file. Column 1 has treatment (1 for cutting speed 1000, 2 for cutting speed 1200, 3 for cutting speed 1400), column 2 has x=hardness, column 3 has y=amount of metal removed.
1 125 77.4
1 120 68.4
1 140 90.4
1 150 97.9
1 136 87.6
2 133 85.4
2 140 94.4
2 125 74
2 120 64.8
2 165 112.1
3 130 79.6
3 175 117.6
3 132 82.3
3 141 91.9
3 124 72.9


Do an analysis of these data and include the following.
1. A scatterplot of the ys versus the xs, using different symbols (or colours) to distinguish the points corresponding to different cutting speeds. Do the ys appear to be related to the xs? Include regression lines of y versus x for each cutting speed. Does it seem reasonable to believe that these three lines have the same slope?
2. An ANCOVA table.
3. An ANOVA table based on the ys, disregarding the xs, to determine whether there are differences in the (mean) amount of metal removed for different cutting speeds. Comment on differences with part (2).

You will be asked a few questions concerning the analysis.

Please use 3 decimal places for the answers below which are not integer-valued.


Part a)
The type II SS for cutting speed (treatment) is______ and its degree of freedom is______    

Part b)
The MSE for ancova is:______    and its degree of freedom is______    

Part c)
The appropriate F ratio for cutting speed is:
______  ​

Part d)
What is the estimate slope for x=hardness?
______  

One in four adults is currently on a diet. You randomly select ten adults and ask them if they are currently on a diet. Find the probability that the number who say they are currently on a diet is (a) exactly three, (b) at least three, (c) more then three, (d) at most four, and (e) less than six.