Park Rangers in a Yellowstone National Park have determined that fawns less than 6 months old have a body weight that is approximately normally distributed with a mean µ = 26.1 kg and standard deviation σ = 4.2 kg. Let x be the weight of a fawn in kilograms. Complete each of the following steps for the word problems below:  Rewrite each of the following word problems into a probability expression, such as P(x>30).  Convert each of the probability expressions involving x into probability expressions involving z, using the information from the scenario.  Sketch a normal curve for each z probability expression with the appropriate probability area shaded.  Solve the problem.

1. What is the probability of selecting a fawn less than 6 months old in Yellowstone that weighs less than 25 kilograms?

2. What is the probability of selecting a fawn less than 6 months old in Yellowstone that weighs more than 19 kilograms?

3. What is the probability of selecting a fawn less than 6 months old in Yellowstone that weighs between 30 and 38 kilograms?

4. If a fawn less than 6 months old weighs 16 pounds, would you say that it is an unusually small animal? Explain and verify your answer mathematically.

5. What is the weight of a fawn less than 6 months old that corresponds with a 20% probability of being randomly selected? Explain and verify your answer mathematically.

Decision analysis. After careful testing and​ analysis, an oil company is considering drilling in two different sites. It is estimated that site A will net ​$20 million if successful​ (probability.2) and lose ​$4 million if not​ (probability.8​);site B will net ​$60 million if successful​ (probability.1) and lose ​$5 million if not​ (probability.9​). Which site should the company choose according to the expected return from each​ site?

Three people A, B, and C practice shooting at a target. The probability that A, B,
and C hit the target is 0.9, 0.8 and 0.6, respectively.
1) Now select any one of them at random, what is the probability that the person
selected hits the target?
2) If the person actually hit target, what is the probability that the person selected
is A?
3) If the person selected shoots once more, what is the probability that he hits the
target again?

A stationery store has a box of 30 large fasteners and 20 small fasteners. They randomly choose 20 of fasteners.

1. What is the probability that their sample contains exactly 10 large fasteners? Round your probability to 4-decimal places.












2. What is the probability that their sample contains exactly 10 large and 10 small fasteners or 11 large and 9 small fasteners? Round your probability to 4-decimal places.












  

When Jerome plays darts. The chances they hit the bulls eye is 1/2.

a)Draw a Tree diagram to represent the problem when three darts are thrown.

b)What is the probability three darts in a row hit the bullseye?

c)What is the probability that none of the three hit the bullseye?

d)What is the probability at least one of the three will hit the bullseye?

e)What is the probability exactly 2 of the three hit the bullseye?

A system consists of two components. The probability that the second component functions in a satisfactory manner during its design life is 0.9, the probability that at least one of the two components does so is 0.94, and the probability that both components do so is 0.85. Given that the first component functions in a satisfactory manner throughout its design life, what is the probability that the second one does also? (Round your answer to three decimal places.)

In recent years, 8 months in Turkey "earthquake" is an average of 4.

a) So what is the probability that an earthquake in Turkey next 8 months, 5 times?

b) What is the probability that an earthquake in Turkey 6 times the next 10 months?

c) What is the probability that the next two years more than 3 earthquakes in Turkey?

d) What is the probability that at most 3 earthquakes in Turkey over the next 12 months?

​a) The probability of having a pool or a garage is

nothing.

​b) The probability of having neither a pool nor a garage is

nothing.

​c) The probability of having a pool but no garage is

nothing.

A certain unsavory bar for poker-playing dogs is attended by only two types of dogs: “good dogs” and “bad dogs.” For a randomly selected dog in the bar, the probability it’s a good dog is 40%. The probability the dog smokes, given that it’s a bad dog is 70%; the probability it smokes given that it’s a good dog is 25%.

a) You walk into the bar and observe a dog smoking a pipe. What the probability it is actually a good dog?

Based on a study from the Chronicles of Flippin'' Awesomeness, the probability that Napoleon and Pedro make it to their first period class on time is 0.20. The probability that they make it to their first period class on time, given that they catch the bus is 0.73. The probability that Napoleon and Pedro catch the bus and make it to their first period class on time is 0.47. What is the probability that Napoleon and Pedro catch the bus?

Answer in decimal form. Round to 4 decimal places as needed.