5. Max grabs three marbles from a bag containing five white marbles and six black marbles. What is the probability that exactly two of the marbles are black?

The length of human pregnancies is approximately normal distributed with mean =266 days and Standard Deviation = 16 days ( 20 points ) . Exercise 8.1 What is the probability a randomly selected pregnancy lasts less than 260 days? Suppose a random sample of 20 pregnancies is obtained. Describe the sample distribution the sampling distribution of sample mean of human pregnancies. What is the probability that a random sample of 20 pregnancies has a mean gestation period of 260 days or less? What is probability that a random sample of 50 pregnancies has a mean gestation period of 260 days or less? What is the probability a random sample of size 15 will have a mean gestation period within 10 days of the mean?

When answering each of the following, the random variable Y is normally distributed with a mean of 65 and a standard deviation of 4.

1. The value of z for being able to determine P(Y ≤ 62) is _______

The P(Y ≤ 62) is ________

2. The 2 values of z for being able to determine P( 69 ≤ Y ≤ 74) are _______ and ________

The P( 69 ≤ Y ≤ 74) is _________

3. The value of z for being able to determine P(Y ≥ 72) is _______

The P(Y ≥ 72) is ________

4. The value of z for being able to determine the value of y such that 10% of the values Y are less than that y

Is ________

         The value of y such that 10% of the values Y are less than that y is _________

Suppose you are deciding whether to take Professor Fisher’s class or Professor Savage’s next semester. You happen to know that each professor gives A’s to those scoring above 90 on a final exam and F’s to those scoring below 60. You also happen to know that the distribution of scores on Professor Fisher’s final is approximately normal with a mean of 74 and a standard deviation of 7 and that the distribution of scores on Professor Savage’s final is approximately normal with a mean of 78 and a standard deviation of 18.

a) Produce a sketch of both teachers’ grade distribution. b) Which Professor gives a higher proportion of A’s? Show the calculations to support your answer. c) Which Professor gives a higher proportion of F’s? Show the calculations to support your answer. d) Suppose that Professor DeGroot has a policy of giving A’s to the top 10% of the scores on his final, regardless of the actual scores. If the distribution of scores on his final turns out to be normal with a mean of 69 and a standard deviation of 9, how high does your score have to be to earn an A?

Your leader wants you to evaluate the difference in cycle time between three different offices. Describe the steps you would take in the evaluation in order to provide a report so the leader can take action.

CAN AN EXAMPLE BE GIVEN OTHER THAN THE ONE POSTED ALREADY?

Annual starting salaries for college graduates with degrees in business administration are generally expected to be between $42,000 and $60,600. Assume that a 95% confidence interval estimate of the population mean annual starting salary is desired. (Round your answers up to the nearest whole number.)

What is the planning value for the population standard deviation?

(a)

How large a sample should be taken if the desired margin of error is $500?

(b)

How large a sample should be taken if the desired margin of error is $300?

(c)

How large a sample should be taken if the desired margin of error is $100?

(d)

Would you recommend trying to obtain the $100 margin of error? Explain.

Almost all medical schools in the United States require students to take the Medical College Admission Test (MCAT). To estimate the mean score μ of those who took the MCAT on your campus, you will obtain the scores of an SRS of students. The scores follow a Normal distribution, and from published information you know that the standard deviation is 10.8 . Suppose that, unknown to you, the mean score of those taking the MCAT on your campus is 495 .

In answering the questions, use z‑scores rounded to two decimal places.

(a) If you choose one student at random, what is the probability that the student's score is between 490 and 500 ? Use Table A, or software to calculate your answer.

(Enter your answer rounded to four decimal places.)

probability:

(b) You sample 36 students. What is the standard deviation of the sampling distribution of their average score ¯x ? (Enter your answer rounded to two decimal places.)

standard deviation:

(c) What is the probability that the mean score of your sample is between 490 and 500 ? (Enter your answer rounded to four decimal places.)

probability:

According to a recent survey, the salaries of assistant professors have a mean of $41,750 and a standard deviation of $8000. Assuming that the salaries of assistant professors follow a normal distribution, find the proportion of assistant professors who earn at most $45,000. Round your answer to at least four decimal places.

In a​ survey, 45​% of the respondents stated that they talk to their pets on the telephone. A veterinarian believed this result to be too​ high, so she randomly selected 210 pet owners and discovered that 93 of them spoke to their pet on the telephone. Does the veterinarian have a right to be​ skeptical? Use the alpha equals=0.01 level of significance.

-Because np 0 (1-p 0) = ___ (Choose greater, less, equal) 10, the sample size is (Choose less than, greater than) 5% of the population size, and the sample (Choose can or cannot be reasonably assumed to be random, is given to be or not to be random) the requirements for testing the hypothesis (Choose are, are not) satisfied.

-What are the null and alternative​ hypotheses?

H0: ____versus H1: ____

-Find the test​ statistic, z0

z0: ___

-Find the​ P-value

P-value:___

-Does the veterinarian have a right to be​ skeptical?

A.The veterinarian has a right to be skeptical. There is sufficient evidence to conclude that the true proportion of pet owners who talk to their pets on the telephone is not 45​%.

B.The veterinarian does not have a right to be skeptical. There is not sufficient evidence to conclude that the true proportion of pet owners who talk to their pets on the telephone is 45​%.

C.The veterinarian has a right to be skeptical. There is sufficient evidence to conclude that the true proportion of pet owners who talk to their pets on the telephone is less than 45​%.

D.The veterinarian does not have a right to be skeptical. There is not sufficient evidence to conclude that the true proportion of pet owners who talk to their pets on the telephone is less than 45​%.

Q1. This year, the standard deviation of revenues is higher in our industry. This indicates competitors’ revenues has become more similar to each other. True or False?

Q2.

68% of these firms have ROAs that range between .23 – .04 and .23 + .04

Where is the number .23 coming from? It’s just the mean ROA in our example. Why am I subtracting .04 from or adding .04 to the mean? It is because the first rule says “1 standard deviation”. Therefore, I translate the above information as follows:

Approximately (      ) firms have ROAs between ( ) and (   ).

Q3.  95% of these firms have ROAs that range between .23 – .08 and .23 + .08

Where is the number .23 coming from? It’s just the mean ROA in our example. Why am I subtracting .08 from or adding .8 to the mean? It is because the first rule says “2 standard deviations”. Since one standard deviation is .04, two standard deviations will be .04+.04 = .08. Therefore, I translate the above information as follows:

Approximately, (       ) firms have ROAs between (   ) and ( ).

Q4. 99.7% of these firms have ROAs that range between .23 – .12 and .23 + .12

Where is the number .23 coming from? It’s just the mean ROA in our example. Why am I subtracting .12 from or adding .12 to the mean? It is because the first rule says “3 standard deviations”. Since one standard deviation is .04, three standard deviations will be .04+.04+.04 = .12 Therefore, I translate the above information as follows:

Approximately, (     ) firms have ROAs between ( ) and (   ).

Q5.

In a sample of firms, 1^st quartile of their ROAs is 0.05 and 3^rd quartile is 0.37. Which of the following is(are) outlier(s)?

                                                -1.44      -0.88       -0.15       0.09        0.37       0.59     1.28      1.78      2.95

Answer:

Q1 = (   )          Q3=(    )       IQR = ( ) - (   )= ( )

Lower boundary = ( ) – 3 x ( )= (   )

Upper boundary = ( ) + 3 x (   )=   ( )

Therefore, any number below (   ) or above ( ) will be considered as outliers. In the above case, outlier(s) is(are) (            )

The GRE is a standardized test that students usually take before entering graduate school. According to a document, the scores on the verbal portion of the GRE have mean 150 points and standard deviation 8.75 points. Assuming that these scores are (approximately) normally distributed.

a. Obtain and interpret the quartiles.

b. Find and interpret the 99th percentile.

This has already been answered but one of the first steps includes .67 and I don't understand where .67 came from. My main question isn't so much find the answer, but go into more detail about where .67 comes from. Thank you!

An expert witness for a paternity lawsuit testifies that the length of a pregnancy is normally distributed with a mean of 280 days and a standard deviation of 13 days. An alleged father was out of the country from 246 to 306 days before the birth of the child, so the pregnancy would have been less than 246 days or more than 306 days long if he was the father. The birth was uncomplicated, and the child needed no medical intervention. What is the probability that he was NOT the father? Calculate the z-scores first, and then use those to calculate the probability. (Round your answer to four decimal places.)


What is the probability that he could be the father? (Round your answer to four decimal places.)

1. Using the information below, predict the entrance score exam (PT school) from Baccalaureate GPA for a person with a GPA of 2.9.  

GPA Entrance Exam Score

Mean 2.85 300

SD 0.42 50

Group of answer choices

305.95

324.31

350

need more information

2. What statistic would you use to determine the strength of the relationship between the rankings of school size and tournament rank for a sports team?

Phi

Cramer's V

Pearson Product Moment Correlation

Kendall's Tau

Point Biserial Correlation

3. When constructing a written exam for assessment in the cognitive domain, the first step is to  

a.) define what you want to measure

b.) decide which item format to employ

c. make a list of content areas to be included

4. If 47% of a group missed an item on a multiple-choice test, what would the difficulty index be?

a.) depends on the standard deviation

b.) .47

c. depends on the mean

d.) .53

How do you create a graph in excel from t-test data?

A college physics professor thinks that two of her sections scored differently on the final exam.  

She collects the scores for the two classes and stores them in a file.

We do not know anything about the test score distributions.

Answer the following. Use alpha = 0.05.

a). What is the value of the test statistic?

b). What is the p-value?

c). Is she correct in stating that the final exam scores from the two sections are not equal to each other?

Here are the score sets

Set 1: 74, 79, 65, 58, 67, 61, 63, 64, 62, 72, 66, 58, 66, 63, 61, 73, 77, 68, 62, 67, 81, 80, 58

Set 2: 75, 77, 76, 82, 88, 91, 92, 70, 89, 85, 71, 82, 91, 77, 67, 87, 92, 88, 94, 85, 97, 93, 74