To reduce laboratory​ costs, water samples from five public swimming pools are combined for one test for the presence of bacteria. Further testing is done only if the combined sample tests positive. Based on past​ results, there is a 0.007 probability of finding bacteria in a public swimming area. Find the probability that a combined sample from five public swimming areas will reveal the presence of bacteria. Is the probability low enough so that further testing of the individual samples is rarely​ necessary?

The probability of a positive test result is ???? ​(Round to three decimal places as​ needed.)

One out of four American adults has eaten Pizza for breakfast. If a sample of 20 adults is selected.

1. What type of probability distribution is this situation? ______________

2. None of them has eaten pizza for breakfast. ______________

3. What is the probability of less than 5 have eaten Pizza for breakfast? ___________

4. What is the probability have eaten between 5-10 Pizza for breakfast? ____________

5. What is the probability that more than 9 have eaten Pizza for breakfast? __________

6. Determine the mean of this sample? _____________

7. Determine the standard deviation of this sample _____________
8. How many adults do you expect to eat Pizza in this sample ____________

Answer the following to 4 decimals of accuracy.
On an exam, the average score is 76 with a standard deviation of 6 points  

What is the probability that an individual chosen at random will have a score below 67 on this exam?

What is the probability that an individual chosen at random will have a score above 85 on this exam?

What is the probability that a student will score between 70 and 80 on this exam?

What score does a student need to have in order to be in the top 5% on this exam?

A group of 10 students are selected randomly and their scores are analyzed. What is the probability that the average score in this group is below 74?

Two cards will be dealt, one at a time and without replacement, from a standard deck of 52 playing cards. In a standard deck, there are 4 Jacks. Answer the following:

a) What is the probability the second card dealt will be a Jack?

P(second card will be Jack) = _______

b) What is the probability both cards dealt will be Jacks?

P(both dealt cards will be Jacks) = _______

c) What is the probability neither card dealt will be a Jack

P(neither dealt card will be a Jack) = ________

d) What is the probability that either card deal is a Jack?

P(either dealt card will be a Jack) = ______

In a nursing program, 85% of incoming freshmen nursing students are female while 15% are male.  Recent records indicate that 70% of the entering female students will graduate with a BSN degree, while 90% of the male students will obtain a BSN degree.

Suppose an incoming freshman nursing student is chosen at random. Use a tree diagram or probability formula to find the following.

a. Find the probability the student is female and graduates with a BSN degree.

b. Find the probability the student graduates with a BSN degree.

c. Find the probability the student is a female given that the student graduates with a BSN degree.

Your driving time to work  (continuous random variable) is between 27 and 69 minutes if the day is sunny, and between 47 and 87 minutes if the day is rainy, with a uniform probability density function in the given range in each case.

Assume that a day is sunny with probability  = 0.83 and rainy with probability .

Your distance to work is  = 50 kilometers. Let  be your average speed for the drive to work, measured in kilometers per minute:

Compute the value of the probability density function (PDF) of the average speed  at  = 0.69

Round your answer to five decimal digits after the decimal point.

A telephone survey conducted in Bowie on a low-interest bank credit card that was offered to 400 households. The responses are as tabled.

a) Develop a joint probability table and show the marginal probabilities. (1 points)

b) What is the probability of a household whose income exceeds $60,000 and who rejects the offer? (2 points)

C) If income is  $60,000, what is the probability the offer will be accepted? (2 points)

d) If the offer is accepted, what is the probability that income exceeds $60,000? (2 points)

Suppose systolic blood pressure of 18-year-old females is approximately normally distributed with a mean of 123 mmHg and a variance of 615.04 mmHg. If a random sample of 18 girls were selected from the population, find the following probabilities:

a) The mean systolic blood pressure will be below 109 mmHg.
probability =

b) The mean systolic blood pressure will be above 124 mmHg.
probability =

c) The mean systolic blood pressure will be between 106 and 125 mmHg.
probability =

d) The mean systolic blood pressure will be between 104 and 112 mmHg.
probability =

Zared plays basketball on his high school team. One of the things he needs to practice is his free throws. On his first shot, there is a probability of 0.6 that he will make the basket. If he makes a basket, his confidence grows and the probability he makes the next shot increases by 0.05. If he misses the shot, the probability he makes the next one decreases by 0.05. He takes 5 shots. What is the probability he makes at least 3 shots?

Please answer with a tree diagram and all the outcomes. As simple and clear as possible please

Part 1

The probability of observing a certain event is 0.2. Suppose we make repeated observations until we have observed the desired event three times. What is the probability that we make five observations in order to have observed the desired event three times.? (Round your answer to four decimal places.)

Part 2

A probability of failure on any given trial is given as 0.01.

Use the Poisson approximation to the binomial to find the (approximate) probability of at least five failures in 200 trials? (Round your answer to three decimal places.)