Given a normal distribution with μ = 48 and σ = 5​,

a. What is the probability that X > 42​? ​(Round to four decimal places as​ needed.)

b. What is the probability that X < 43​? ​(Round to four decimal places as​ needed.)

c. For this​ distribution, 9​% of the values are less than what​ X-value? ​(Round to the nearest integer as​ needed.)

d. Between what two​ X-values (symmetrically distributed around the​ mean) are 60​% of the​ values?

​(Round to the nearest integer as​ needed.)

The HR manager of a large department store believes the number of resignations per week of casual staff at the store can be approximated by a normal distribution with a mean of 42 resignations per week and variance 51.1 (resignations per week)2 . From a large amount of historical data available on the HR database regarding weekly resignations of casuals, a sample of 52 weeks was selected. What must the value of the sample mean be so that only 15% of all possible sample means (of size 52) are less than this value? Give your answer correct to 2 decimal places.

In​ baseball, League A allows a designated hitter​ (DH) to bat for the​ pitcher, who is typically a weak hitter. In League​ B, the pitcher must bat. The common belief is that this results in League A teams scoring more runs. In interleague​ play, when League A teams visit League B​ teams, the League A pitcher must bat.​ So, if the DH does result in more​ runs, it would be expected that league A teams will score more runs in League A park than when visiting League B parks. To test this​ claim, a random sample of runs scored by league A teams with and without their DH is given in the accompanying table. Complete parts​ a) through​ d) below.

a) Draw​ side-by-side boxplots of the number of runs scored by League A teams with and without their DH. Choose the correct graph below.

A.

051015AB

Two boxplots, one above the other, share a horizontal axis labeled from 0 to 15 in increments of 1. The bottom boxplot is labeled A and has vertical line segments drawn at 4, 6, and 7. A box encloses the vertical line segments, and horizontal line segments extend from both sides of the box to 0 and 13. An x is plotted at 14. The top boxplot is labeled B and has vertical line segments at 3, 4.5, and 7. A box encloses the vertical line segments, and horizontal line segments extend from both sides of the box to 0 and 11.

B.

051015AB

Two boxplots, one above the other, share a horizontal axis labeled from 0 to 15 in increments of 1. The bottom boxplot is labeled A and has vertical line segments drawn at 4, 6, and 7. A box encloses the vertical line segments, and horizontal line segments extend from both sides of the box to 0 and 9. Three x's are plotted at 12, 13, and 14. The top boxplot is labeled B and has vertical line segments at 2, 3.5, and 6. A box encloses the vertical line segments, and horizontal line segments extend from both sides of the box to 0 and 10.

C.

051015AB

Two boxplots, one above the other, share a horizontal axis labeled from 0 to 15 in increments of 1. The bottom boxplot is labeled A and has vertical line segments drawn at 3, 5, and 6. A box encloses the vertical line segments, and horizontal line segments extend from both sides of the box to 0 and 12. Two x's are plotted at 13 and 14. The top boxplot is labeled B and has vertical line segments at 2, 3.5, and 6. A box encloses the vertical line segments, and horizontal line segments extend from both sides of the box to 0 and 12.

D.

051015AB

Two boxplots, one above the other, share a horizontal axis labeled from 0 to 15 in increments of 1. The bottom boxplot is labeled A and has vertical line segments drawn at 4, 6, and 7. A box encloses the vertical line segments, and horizontal line segments extend from both sides of the box to 1 and 14. The top boxplot is labeled B and has vertical line segments at 2, 3.5, and 6. A box encloses the vertical line segments, and horizontal line segments extend from both sides of the box to 0 and 12.

Does there appear to be a difference in the number of runs between these​ situations?

A. No but the number of runs scored in a League A park appear to be slightly higher than the number of runs scored in a League B park.

B. Yes because the number of runs scored in a League B park appear to have a higher median than the number of runs scored in a League A park.

C.Yes because the number of runs scored in a League A park appear to have a higher median than the number of runs scored in a League B park.

D.No because the number of runs scored in a League A park is about the same as the number of runs scored in a League B park.

​b) Explain why a hypothesis test may be used to test whether the mean number of runs scored for the two types of ballparks differ.

Select all that apply.

A.Each sample has the same sample size.

B.Each sample is obtained independently of the other.

C.Each sample size is small relative to the size of its population.

D.Each sample is a simple random sample.

E.Each sample size is large.

​c) Test whether the mean number of runs scored in a League A park is greater than the mean number of runs scored in a League B park at the

alphaα=0.05 level of significance.

Determine the null and alternative hypotheses for this test. Let mu Subscript Upper AμA

represent the mean number of runs scored by a League A team in a League A park and let

mu Subscript Upper BμB represent the mean number of runs scored by a League A team in a League B park.

Upper H 0H0​:

▼

sigma Subscript Upper AσA

pp mu Subscript Upper AμA

▼

greater than>

equals=

less than<

not equals≠

▼

sigma Subscript Upper BσB

mu Subscript Upper BμB

p 0p0

versus

Upper H 1H1​:

▼

mu Subscript Upper AμA

pp

sigma Subscript Upper AσA

▼

greater than>

equals=

less than<

not equals≠

▼

p0 mu Subscript Upper BμB sigma Subscript Upper BσB Find t0​,the test statistic for this hypothesis test. t0=nothing

​(Round to two decimal places as​ needed.)

Determine the​ P-value for this test.

​P-value=

​(Round to three decimal places as​ needed.)

State the appropriate conclusion. Choose the correct answer below.

A.Do not reject Upper H0. There is not sufficient evidenceThere is not sufficient evidence at the level of significance to conclude that games played with a designated hitter result in more runs.

B.Reject Upper H 0H0.There is not sufficient evidence at the level of significance to conclude that games played with a designated hitter result in more runs.

C.Do not reject Upper H0.There is sufficient evidenceat the level of significance to conclude that games played with a designated hitter result in more runs.

D.Reject Upper H0. There is sufficient evidenceThere is sufficient evidence at the level of significance to conclude that games played with a designated hitter result in more runs.

​d) Construct a 95​% confidence interval for the mean difference in the number of runs scored by League A teams in a League A park and the number of runs scored by League A teams in a League B park. Interpret the interval.

Lower​ bound:

Upper​ bound:

​(Round to three decimal places as​ needed.)

Interpret the confidence interval. Select the correct choice below and fill in the answer boxes to complete your choice.

​(Round to three decimal places as needed. Use ascending​ order)

A. We are 95​%confident the difference between the mean number of runs scored in a League A park and the mean number of runs scored in a League B park is between nothing and nothing.The confidence interval does not containdoes not contain ​zero, so there is sufficient evidence to conclude there is a difference in the mean number of runs scored with or without the DH.

B. We are 95​% confident the difference between the mean number of runs scored in a League A park and the mean number of runs scored in a League B park is between nothing and nothing.The confidence interval contains ​zero, so there is notis not sufficient evidence to conclude there is a difference in the mean number of runs scored with or without the DH.

Practitioners measured spiritual well-being (SWB) in a sample of 16 adults who were alcoholic before and following treatment for alcoholism.

Use the normal approximation for the Wilcoxon signed-ranks T test to analyze the data above. (Round your answer to two decimal places.)
z =  

State whether to retain or reject the null hypothesis. (Assume alpha equal to 0.05.)

A researcher working for an insurance company that sells life insurance would like to use regression analysis to predict life expectancy of his clients. He knows that there are several factors that contribute to life expectancy: some are genetic, some are related to life style, some are related to biological factors, and some are related to environment (access to health care, cleanliness of air, etc.) . He selects these candidate variables to develop his regression equation: gender, number of cigarettes smoked per day, cholesterol level, systolic blood pressure, and height-to-weight index: (actual weight / appropriate weight given gender, build, and height) * 100. Use the datasheet life expectancy in datasetsRM.xls to develop a regression equation to predict how long a person should live (for gender: 0=female, 1=male): 1. First, plot each non-categorical predictor variable against the dependent variable (age of death) and examine the plot to see if the relationship is linear. What’s your assessment? 2. Perform a multiple regression analysis and write up the results of your regression analysis in APA style. 3. For a male who does not smoke cigarettes at all, has a systolic blood pressure of 130, a height-to-weight index of 110, and a cholesterol level of 200, what is his life expectancy? NumCigsDay WtHtIndex Gender Cholesterol BloodPres AgeOfDeath 0 98 0 179 120 90 0 90 0 186 100 98 0 140 0 190 130 90 3 96 0 191 120 87 0 120 0 200 120 90 0 100 0 187 120 94 0 130 0 190 110 96 4 92 0 191 110 83 5 110 0 200 110 79 5 193 0 210 120 79 10 107 0 215 130 77 0 117 0 227 140 80 0 128 0 240 130 99 15 179 0 230 150 68 10 150 0 240 160 70 5 100 0 245 120 79 8 112 0 260 130 76 10 150 0 275 140 67 8 121 0 280 130 72 0 90 1 210 120 85 0 100 1 187 100 94 0 130 1 179 130 88 10 92 1 183 120 72 0 119 1 184 120 89 0 110 1 189 120 80 2 120 1 192 110 87 6 100 1 196 110 69 4 140 1 204 110 73 10 128 1 215 120 65 0 107 1 216 140 85 0 98 1 219 130 75 8 119 1 220 140 68 3 117 1 222 130 89 11 193 1 232 150 62 12 179 1 245 160 66 8 150 1 246 120 78 12 96 1 261 130 67 0 121 1 269 130 70 8 112 1 279 140 64 0 150 1 280 130 74

1. In our sample of 42 students, we are interested in whether the amount of money students think a first date should cost is different based on whether they are in a romantic relationship or not. The mean amount stated by the 21 students in a relationship was $58.81, with a standard deviation of $47.17, while the 21 students not in a relationship thought first dates should cost a mean of $48.10 with a standard deviation of $24.16. State the null and alternative hypotheses, conduct the appropriate type of t test, and write a conclusion interpreting your findings.

A transect is an archaeological study area that is mile wide and 1 mile long. A site in a transect is the location of a significant archaeological find. Let x represent the number of sites per transect. In a section of Chaco Canyon, a large number of transects showed that x has a population variance . In a different section of Chaco Canyon, a random sample of 25 transects gave a sample variance for the number of sites per transect. Use an alpha = 0.1 to test the claim that the variance in the new section is greater than 37.9. Given 0.05 < P-Value < 0.1, will you reject or fail to reject the null hypothesis of independence? ​ Select one:

a. Since the P-Value is less than the level of significance, we reject the null hypothesis that the variance is equal to 37.9. At 0.1 level of significance, we conclude that the variance is greater than 37.9.

b. Since the P-Value is less than the level of significance, we fail to reject the null hypothesis that the variance is greater than 37.9. At 0.1 level of significance, we conclude that the variance is equal to 37.9.

c. Since the P-Value is greater than the level of significance, we fail to reject the null hypothesis that the variance is greater than 37.9. At 0.1 level of significance, we conclude that the variance is equal to 37.9.

d. Since the P-Value is greater than the level of significance, we fail to reject the null hypothesis that the variance is equal to 37.9. At 0.1 level of significance, we conclude that the variance is greater than 37.9.

e. Since the P-Value is less than the level of significance, we fail to reject the null hypothesis that the variance is equal to 37.9. At 0.1 level of significance, we conclude that the variance is greater than 37.9.

Discuss in 300 words regression, analysis, assumptions?

can you please type it, it is really hard to read some handwriting?

Assume that females have pulse rates that are normally distributed with a mean of mu equals 73.0 beats per minute and a standard deviation of sigma equals 12.5 beats per minute.

Complete parts​ (a) through​ (c) below.

. If 1 adult female is randomly​ selected, find the probability that her pulse rate is between

6666

beats per minute and

8080

beats per minute.

You and two friends are on a game show. Each of you enters the studio with a hat on your head. There are two colors of hats: red and blue. They are assigned randomly, so each person has a 50% chance of a red hat and a 50% chance of a blue hat. Each person can see the hats of the two other people, but they can't see their own hat. Each person can either try to guess the color of his or her own hat or pass. All three of you do it simultaneously, so there is no way to base your guess on the guesses of your friends. If nobody guesses incorrectly and at least one person guesses correctly, then you all share a big prize. Otherwise you all lose. If everybody randomly guesses and nobody passes what is the probability that you will win?

Since you are all friends, and you all know how the game works, you develop a strategy with your friends before the show to maximise your probability of winning. (Note: if your strategy requires a particular person to speak regardless of what hat colours you all see then that person is you. In cases where both colours are equally attractive then you will pick red.)
When you walk onto the stage you can see that both of your friends have blue hats on.
What colour should you guess?
(a) Red (b) Blue (c) Stay silent

When you walk onto the stage you can see that one of your friends has a red hat on and the other friend has a blue hat on. What colour should you guess? (
a) Red (b) Blue (c) Stay Silent
What is the probability that you will win using the best strategy?

Low birth weights are considered to be less than 2500 g for newborns. Birth weights are normally distributed with a mean of 3150 g and a standard deviation of 700 g.

a) If a birth weight is randomly selected what is the probability that it is a low birth weight?

b) Find the weights considered to be significantly low using the criterion of a probability of 0.02 or less. That is, find the weight ranked as the lowest 2%.

c) Find the weight ranked as the highest 2%

d) Find the probability of a birth weight between 2600 g and 3500 g.

Can someone please describe the relationship between f-value/ratio, p-value, and alpha value (0.05) in the ANOVA and provide a good example

The town of KnowWearSpatial, U.S.A. operates a rubbish waste disposal facility that is overloaded if its 4680 households discard waste with weights having a mean that exceeds 27.22 lb/wk. For many different weeks, it is found that the samples of 4680 households have weights that are normally distributed with a mean of 26.95 lb and a standard deviation of 12.13 lb. What is the proportion of weeks in which the waste disposal facility is overloaded? P(M > 27.22) = Enter your answer as a number accurate to 4 decimal places. NOTE: Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted. Is this an acceptable level, or should action be taken to correct a problem of an overloaded system? Yes, this is an acceptable level because it is unusual for the system to be overloaded. No, this is not an acceptable level because it is not unusual for the system to be overloaded.m

A new LED light to replace incandescent bulbs has come on the market. The box says it has an average life of 8000 hours with a standard deviation of 200 hours.

A.) What is the probability that a single bulb will last between 7950 and 8100 hours?

B.) What is the probability that the mean of a sample of 75 bulbs picked at random will be between 7950 and 8100 hours?

An auditor for a hardware store chain wished to compare the efficiency of two different auditing techniques. To do this he selected a sample of nine store accounts and applied auditing techniques A and B to each of the nine accounts selected. The number of errors found in each of techniques A and B is listed in the table below:

Select a 90% confidence interval for the true mean difference in the two techniques.

a) [0.261, 8.627]

b) [-4.183, 4.183]

c) [2.195, 6.693]

d) [3.050, 5.838]

e) [2.584, 6.304]

f) None of the above