The time needed to complete a final examination in a particular college course is normally distributed with a mean of 83 minutes and a standard deviation of 13 minutes. Answer the following questions. Round the intermediate calculations for z value to 2 decimal places. Use Table 1 in Appendix B. What is the probability of completing the exam in one hour or less (to 4 decimals)? What is the probability that a student will complete the exam in more than 60 minutes but less than 75 minutes (to 4 decimals)? Assume that the class has 60 students and that the examination period is 90 minutes in length. How many students do you expect will be unable to complete the exam in the allotted time (to the next whole number)?

A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 36.3 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 36.3 weeks and that the population standard deviation is 7.5 weeks. Suppose you would like to select a random sample of 124 unemployed individuals for a follow-up study.

Find the probability that a single randomly selected value is between 35.8 and 36.1. P(35.8 < X < 36.1) =

Find the probability that a sample of size n=124 is randomly selected with a mean between 35.8 and 36.1. P(35.8 < M < 36.1) =

Enter your answers as numbers accurate to 4 decimal places.

Part 1: Seventeen items are found in a box, eight of which are observed to exhibit a particularly desirable property. Suppose six of these items are randomly selected from the box without replacement and let X be the random variable representing the number among the six that exhibit the desirable property.

Compute (round answer to four decimal places) P(X = 4) =

Part 2 : The probability of observing a certain event is 0.4. Suppose we make repeated observations until we have observed the desired event two times.What is the probability that we make four observations in order to have observed the desired event two times.? (Round your answer to four decimal places

Dr. Frankenstein relies on lightning strikes to power his resurrection machine. Lightning strikes his machine at a fairly consistent rate across all thunderstorms. The average number of strikes during a two-hour storm is 17. Further, each strike is roughly independent; that is, the probability of a strike is unrelated to how recently another strike occurred. If he needs at least seven strikes to generate enough energy to resurrect his monster, but his machine will overload and breakdown if it gets more than ten strikes.

What is the probability that, after a two-hour storm, he will be able to resurrect his monster? Assume that he waits until the storm ends before attempting to run the machine.

A logistic regression model describes how the probability of voting for the Republican candidate in a U.S. presidential election depends on x_1=family income, x_2=number of years of education, and s=sex (1=male, 0 = female), the prediction equation is "logit"[P ̂ (y=1)] = -2.40+0.02(x_1) +0.08(x_2)+0.20s.

For this sample, ranges from 6 to 157 with a standard deviation of 25, and ranges from 7 to 20 with a standard deviation of 3.

1. Interpret the sign of the coefficients of income and years of education.
2. Find the estimated probability of voting Republican for (i) a man with 16 years of education and income 30 thousand dollars, (ii) a woman with 16 years of education and income 30 thousand dollars.

A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 12.3 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 12.3 weeks and that the population standard deviation is 5.5 weeks. Suppose you would like to select a random sample of 99 unemployed individuals for a follow-up study. Find the probability that a single randomly selected value is between 13.7 and 14. P ( 13.7 < x < 14 ) = Find the probability that a sample of size n = 99 is randomly selected with a mean between 13.7 and 14. P ( 13.7 < ¯ x < 14 ) = Enter your answers as numbers accurate to 4 decimal places.

The time needed to complete a final examination in a particular college course is normally distributed with a mean of 79 minutes and a standard deviation of 8 minutes. Answer the following questions. Round the intermediate calculations for z value to 2 decimal places.

1. What is the probability of completing the exam in one hour or less (to 4 decimals)?
   
2. What is the probability that a student will complete the exam in more than 60 minutes but less than 75 minutes (to 4 decimals)?
   
3. Assume that the class has 60 students and that the examination period is 90 minutes in length. How many students do you expect will be unable to complete the exam in the allotted time (to the next whole number)?

I need to understand how to do this in excel.

(a) There are 5 boys and 2 girls waiting in a straight line for the school bus. How many ways
can the queue be arranged such that two girls are not standing next to each other?
(b) There are 7 boys and 5 girls to be assigned into different groups. Answer the following:
i) Suppose that the 12 people are divided into 3 groups so that the number of people
in each group is 2, 4, and 6. How many ways can you assign the people?
ii) Suppose 6 people are randomly chosen without replacement. What is the
probability that 3 of them are boys and 3 are girls?
iii) Suppose 5 people are randomly chosen without replacement. What is the
probability that at least 3 of them are girls?

A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 14.9 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 14.9 weeks and that the population standard deviation is 6.2 weeks. Suppose you would like to select a random sample of 208 unemployed individuals for a follow-up study.

Find the probability that a single randomly selected value is between 14.7 and 16.1.
P(14.7 < X < 16.1) =

Find the probability that a sample of size n=208 is randomly selected with a mean between 14.7 and 16.1.
P(14.7 < M < 16.1) =

Enter your answers as numbers accurate to 4 decimal places.