Statistics and Probability Answers

A Math professor must choose a schedule of four classes to teach, where two are chosen from a list of 24 Algebra classes, one is chosen from a list of 12 Statistics classes, and one is chosen from a list of 4 Calculus classes. In how many ways can the professor choose a different schedule.

The nicotine contents of five cigarettes of a serration brand, measured in milligrams, are 21, 19, 23, 19, 23. Establish a 99% confidence interval estimate of the average nicotine content of this brand of cigarette.

7. Which of the following bank accounts has the highest effective annual return?

a. An account that pays 8% nominal interest with monthly compounding.
b. An account that pays 8% nominal interest with annual compounding.
c. An account that pays 7% nominal interest with daily (365-day) compounding.
d. An account that pays 7% nominal interest with monthly compounding.
e. An account that pays 8% nominal interest with daily (365-day) compounding.

Use the confidence level and sample data to find a confidence interval for estimating the population mean.
A group of 56 randomly selected students have a mean score of 30.8 with a standard deviation of 4.5 on a placement test. What is the 90% confidence interval for the mean score, of all students taking the test?

acme educators knows that the average test grade for its certification exams is 82 and the standard deviation for these is 12 points. what are the grades for the top 50% of test takers? what are the grades for the top 15%? what percent of test takers are expected to score below 90? what is the probability that a test taker will score under 75?

A bag contains 3 coin, one of which is coined with two heads while the other coin are normal and not biased. A coin is chosen at random from the bag and tossed four times in succession . If heads turn up each time, what is the probability that this is the two- headed coin?

Suppose that we have two urns, 1 and 2, each with two drawers. Urn 1 has a gold coin in one drawer and a silver coin in the other drawer which urn 2 has a gold coin is each drawer. One urn is chosen at random; then a drawer is chosen at random from the chosen urn. The coin found in drawer turns out to be gold . What is the probability that the coin came from urn 2?

There are n stations in a slotted LAN. Each station attempts to transmit with a probability p in each time slot. What is the probability that only one station transmits in a given time slot?

a) np(1-p)^(n-1)
b)(1-p)^(n-1)
c)p(1-p)^(n-1)
d)1-(1-p)^(n-1)

I need help to understand what is the statistically best way to calculate the total probability if I have the below scenario.
100 activities are scheduled with 50% probability of completion for the baseline activity duration.
We are one third through the project and 30 activities are complete.
For each of the completed activities the actual duration is projected on the baseline probability distribution to find out at what % probability the actual duration occurred.
the intent is to find the total probability of all the activities including the actual activities (ofcourse the probability for incomplete activities remain at 50% probability)
what is the best way to calculate the total probability.
The reason why we use all activities is so that the total calculated probability would be influenced more by the incomplete activities and less by actual activities at the beginning of the project and that influence is increased as the schedule progresses.
Any help is appreciated. Thank you.

Suppose there are N = 10 urns behind a curtain, such that you cannot see them. The urns are numbered from i = 1,…, 10. Urn i contains ten balls: i white balls and 10 - i red balls. A person behind the curtain picks one urn at random (all urns are equiprobable), picks ten balls with replacement from this urn and notes the result. Afterwards, the person tells you that NW = 3 white balls were drawn (and accordingly 10 - 3 = 7 red balls). What is the probability that the person has chosen urn i ∈ {1, 2,…,10}? Please give a derivation and numbers.