8. A plane is missing and is presumed to have probability of i/6 of being down in one of three regions, i=1,2,3. If a plane is actually down in region i, suppose there is a probability of 1- i/6 that the plane will be found upon a search of the i-th region. a) What is the probability the plane is in region 3, given a search of region 3 did not find the plane? b) What is the probability the plane is in region 1, given a search of region 2 did not find the plane?

A recent survey of 1016 employees found that 29​% of them would lay off their bosses if they could. Complete parts a through d below based on a random sample of 10 employees.

a. What is the probability that exactly three employees would lay off their​ boss? The probability is

b. What is the probability that three or fewer employees would lay off their​ bosses?

c. What is the probability that five or more employees would lay off their​ bosses?

d. What are the mean and standard deviation for this​ distribution?

When conducting an interview with a group of people in order to enter a television program, it is found that 30% of 1500 people do not meet the required requirements. 34 people are interviewed.
a)   What is the probability that less than 24 meet the required requirements?
b)   What is the probability that 14 to 27 do not meet the required requirements?
c)   What is the probability that more than 26 meet the required requirements?
d)   What is the probability that less than 23 or more than 29 do not meet the required requirements?

A new car that is a gas- and electric-powered hybrid has recently hit the market. The distance travelled on 1 gallon of fuel is normally distributed with a mean of 45 miles and a standard deviation of 7 miles. Find the probability of the following events:

A. The car travels more than 50 miles per gallon.

Probability =

B. The car travels less than 40 miles per gallon.

Probability =

C. The car travels between 37 and 51 miles per gallon.

Probability =

A flycatcher is trying to catch passing bugs and will keep going until it gets one, or until it has tried five times, whichever comes first. The probability that it catches a bug on any given try is 20%, and each try is independent.

a) What is the probability that it catches its first bug on an even-numbered attempt?

b) What is the probability that it catches its first bug on an odd-numbered attempt?

c) What is the probability that the bird gives up before catching a fly?

1. In the pine tree forest, the probability that a randomly chosen tree is a high producer, that is, it has more than 60 cones, is 0.46.

1. If a forester selects trees until he finds one that is a high producer, what is the probability that he selects more than 2 trees?
2. Suppose the forest contains 2000 trees, use a normal approximation to find the probability that fewer than 950 of them are high producers.
3. Use software ( a calculator) to find the probability in b exactly. Compare your results.

A certain weightlifter is prone to back injury. He finds that he has a 20% chance of hurting his back if he uses the proper form of bending at the hips and keeping his spine locked. The probability that he will hurt his back with bad form is 95%. The probability that he uses proper form is 75%.

A. What is the probability that he doesn't hurt his back and has proper form?

B. What is the probability he doesn't hurt his back?

1. Suppose the scores on a chemistry test were normally distributed with a mean of 78 and a standard deviation of 10. If a student who completed the test is chosen at random,

a. Find the probability that the student earned fewer than 75 points.

b. Find the probability that the student earned at least 70 points.

c. Find the probability that the student earned between 80 and 90 points.

d. Find the probability that the student earned either less than 80 points or more than 90 points.

3. Rosa Diaz is one of the best detectives at the 99th precinct in Brooklyn. She averages 4.89 felony arrests a week. Assume a 5-day workweek.

   1. A) What is the probability that Rosa has 5 felony arrests in a week?

   2. B) What is the probability that Rosa has at least 3 felony arrests in a week?

   3. C) What is the probability that Rosa has between 5 and 10 felony arrests in a week exclusive?

   4. D) What is the probability that Rosa has 3 felony arrests in a day?

The ages of a group of 50 women are approximately normally distributed with a mean of 51 years and a standard deviation of 6 years. One woman is randomly selected from the​ group, and her age is observed.

a. Find the probability that her age will fall between 56 and 61 years.

b. Find the probability that her age will fall between 48 and 51 years.

c. Find the probability that her age will be less than 35 years

. d. Find the probability that her age will exceed 40 years.