Statistics and Probability Answers

The following line was given in a solution to a question.
P(A)= (6C3 x 43C3 ) + ( 6C4 x 43C2 ) divided by 49 6

What might the question have been? Be sure to identify and explain everything that you know is true about the question.

The dance team has 9 dancers to perform different roles in each performance.
The probability that the team selects the same order as last performance is 1 divided by 362880 . A) Explain where each the numerator and denominator come from.
B) What is the probability that the team puts the top hip hop dancer in the third position and top break dancer in the first position? Assume these are not the same people.
C) Create a question, related to the dancers, where you use the indirect method, n(A’), to solve.

If x is 7.35 and x(0.05) is 9.5 then please explain how is it possible that x>x(0.05) ?

A random sample of eight drugstores shows the following prices (in $ of a popular pain reliever:
3.50, 4.00, 2.00, 3.00, 2.50, 3.50, 2.50, 3.00
2.50 3.00
a. What is the standard deviation for the sample?
b.Assume the normal distribution for the underlying population to construct the 90% confidence interval for the population mean.

A Family is relocating from St. Louis, Missouri, to California. Due to an increasing inventory of houses in St. Louis, it is taking longer than before to sell a house. The wife is concerned and wants to know when it is optimal to put their house on the market. Her realtor friend informs them than the last 26 houses that sol in their neighborhood took an average time of 218 days to sell. The realtor also tells them that based on her prior experience, the population standard deviation is 72 days.
a. What assumption regarding the population is necessary for making an interval estimate for the population mean? (2 Marks)
b. Construct the 90% confidence interval for the mean sale time for all homes in the neighborhood. (4 Marks)

Customers arrive at a drive-through teller window of a bank. They stay in line when the teller is busy. The service time is exponentially distributed with a mean of four minutes.
a. What is the probability that the next customer in line will take longer than seven minutes to be served? (2 Marks) b. What is the probability that the next customer in line will take less than eight minutes to be served? (2 Marks) c. What is the probability that the next customer in line will take between three and six minutes to be served? (4 Marks)

A class has 40 students. Each student is assigned a distinct number from 1 to 40. Four students will be selected at random. Find the probability of the event that the first student selected is assigned a number from 1 to 10, the second student selected is assigned a number from 11 to 20, the third student selected is assigned a number from 1 to 10, and the fourth student selected is assigned a number from 11 to 20 under the following sampling schemes:

a) random sampling with replacement
b) random sampling without replacement

Two cards are drawn from a well shuffled pack of 52 playing cards. Calculate the probability of the
events (i) there is one card of black suits and other of red suits, (ii) both the card are aces (iii)
both the cards are hearts