The mean number of words per minute (WPM) read by sixth graders is 99 with a variance of 441. If 82 sixth graders are randomly selected, what is the probability that the sample mean would differ from the population mean by less than 3.69 WPM? Round your answer to four decimal places.

-What is the expected number of pairs of players that lose in the first round

-John, Ron, Don, Maya have decided that they will only look at one of the others in their group of 4 in the first round, if the same person is looking at each other they lose. what is the probability that all four of them end up losing.

Annual votes for a small political party are approximately normally distributed with a mean of 50 000 and a standard deviation of 20 000.

a. What number of total votes would be needed by a party to fall in the lowest 30%?

b. What is the probability of having an above average vote range of between R60000 to R80000?

Suppose we have a sack with 2 red balls and 2 black balls, and we draw balls without replacement until the second red ball is drawn.

Describe the random variable ? = "the number of balls drawn".

Describe by giving the range, probability distribution, expected value, standard deviation, and variance.

About 96 percent of the very largest colleges and universities offer distance learning courses. Suppose you are to randomly select 20 such institutions and count the number (denoted by X) that offer distance learning courses.

The probability that at most seventeen offer such courses is _____________ . (Round your answer to four decimal places.)

The probability that a randomly selected person is left-handed is 0.1. Suppose we are to randomly select 10 people. Let X be the number of people selected out of the 10 that are left-handed. Find the following probabilities:

(a) P(X = 2) =

(b) P(X ≤ 2) =

(c) P(X > 2) =

Assume that the mean of the engineered part is 79.95 and standard deviation of 0.017291, with a lower specification limit of 79.9 and upper specification limit of 80.

a. Determine the probability that a part is defective.

b. Suppose that 1,000,000 parts are produced, what is the expected number of defective units? This is equivalent to finding the PPM (parts per million).

1. A bowl of Halloween candy contains 20 KitKats and 35 Snickers. You are getting ready to grab 2 pieces of candy from the bowl without looking. Create a probability distribution where the random variable, x, represents the number of Snickers picked. (You can treat the probabilities as with replacement).

According to an airline, flights on a certain route are NOT on time 15% of the time. Suppose 10 flights are randomly selected and the number of NOT on time flights is recorded. Find the probability of the following question.

A) At least 3 flights are not on time.

B) At the most 8 flights are on time.

C) In between 6 and 9 flights are on time.