The random variable x is the number of occurrences of an event over an interval of ten minutes. It can be assumed that the probability of an occurrence is the same in any two-time periods of an equal length. It is known that the mean number of occurrences in ten minutes is 5.3. The probability that there are 8 occurrences in ten minutes is

Forty-three percent of US teens have heard of a fax machine. You randomly select 12 US teens. Find the probability that the number of these selected teens that have heard of a fax machine is exactly six (first answer listed below). Find the probability that the number is more than 8 (second answer listed below).

You know that there is a problem in your car due to sounds you hear when driving. There can be only two sources for the problem 1) Brakes 2) Engine. You are estimating that the problem is due to brakes with probability 0.6, and it is due to engine with probability 0.4. Furthermore, if the problem is due to brakes or engine, the number of miles you can drive without any repair is exponentially distributed with mean 500 and 100 miles, respectively.

a) What is the probability that the number of miles you can drive the car without any repair is larger than 200 miles.?

b)What is the expected number of miles you can drive the car without any repair?

A. 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. At least 3 flights are not on time.

B. 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. At the most 8 flights are on time.

c. 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. In between 6 and 9 flights are on time.

An airport limousine can accommodate up to four passengers on any one trip. The company will accept a maximum of six reservations for a trip, and a passenger must have a reservation. From previous records, 50% of all those making reservations do not appear for the trip. Answer the following questions, assuming independence wherever appropriate. (Round your answers to three decimal places.)

(a) If six reservations are made, what is the probability that at least one individual with a reservation cannot be accommodated on the trip?

.109

(b) If six reservations are made, what is the expected number of available places when the limousine departs?
1.125

(c) Suppose the probability distribution of the number of reservations made is given in the accompanying table.

Let X denote the number of passengers on a randomly selected trip. Obtain the probability mass function of X.

1) Assume that a procedure yields a binomial distribution with nequals5 trials and a probability of success of pequals0.30. Use a binomial probability table to find the probability that the number of successes x is exactly 1.

2) Assume that random guesses are made for 7 multiple choice questions on an SAT​ test, so that there are n=7 trials

​trials, each with a probability of success​ (correct) given by p=0.2 Find the probability that the number x of correct answers is fewer than 4.

3) Assume that when adults with smartphones are randomly​ selected, 42% use them in meetings or classes. If 6 adult smartphone users are randomly​ selected, find the probability that at least 3 of them use their smartphones in meetings or classes. The probability is ?

4) Based on a​ survey, assume that 47% of consumers are comfortable having drones deliver their purchases. Suppose that we want to find the probability that when 4 consumers are randomly​ selected, exactly 2 of them are comfortable with delivery by drones. Identify the values of​ n, x,​ p, and q.

The value of n is

TV sets: According to the Nielsen Company, the mean number of TV sets in a U.S. household in 2013 was 2.24. Assume the standard deviation is 1.2. A sample of 80 households is drawn. Use the Cumulative Normal Distribution Table if needed. Part 1 of 5 What is the probability that the sample mean number of TV sets is greater than 2? Round your answer to four decimal places. The probability that the sample mean number of TV sets is greater than 2 is . Part 2 of 5 What is the probability that the sample mean number of TV sets is between 2.5 and 3? Round your answer to four decimal places. The probability that the sample mean number of TV sets is between 2.5 and 3 is . Part 3 of 5 Find the 20th percentile of the sample mean. Round your answer to two decimal places. The 20th percentile of the sample mean is . Part 4 of 5 Would it be unusual for the sample mean to be less than 2? Round your answer to four decimal places. It ▼(Choose one) unusual because the probability of the sample mean being less than 2 is . Part 5 of 5 Do you think it would be unusual for an individual household to have fewer than 2 TV sets? Explain. Assume the population is approximately normal. Round your answer to four decimal places. It ▼(Choose one) be unusual for an individual household to have fewer than 2 TV sets, since the probability is .

TV sets: According to the Nielsen Company, the mean number of TV sets in a U.S. household in 2013 was 2.24. Assume the standard deviation is 1.4. A sample of 80 households is drawn. Use the Cumulative Normal Distribution Table if needed. Part 1 of 5 What is the probability that the sample mean number of TV sets is greater than 2? Round your answer to four decimal places. The probability that the sample mean number of TV sets is greater than 2 is . Part 2 of 5 What is the probability that the sample mean number of TV sets is between 2.5 and 3? Round your answer to four decimal places. The probability that the sample mean number of TV sets is between 2.5 and 3 is . Part 3 of 5 Find the 40th percentile of the sample mean. Round your answer to two decimal places. The 40th percentile of the sample mean is . Part 4 of 5 Would it be unusual for the sample mean to be less than 2? Round your answer to four decimal places. It ▼(Choose one) unusual because the probability of the sample mean being less than 2 is . Part 5 of 5 Do you think it would be unusual for an individual household to have fewer than 2 TV sets? Explain. Assume the population is approximately normal. Round your answer to four decimal places. It ▼(Choose one) be unusual for an individual household to have fewer than 2 TV sets, since the probability is .