An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 120 lb and 161 lb. The new population of pilots has normally distributed weights with a mean of 129 lb and a standard deviation of 29.1 lb.

a. If a pilot is randomly​ selected, find the probability that his weight is between 120 lb and 161 lb. The probability is approximately _____. ​(Round to four decimal places as​ needed.)

b. If 37 different pilots are randomly​ selected, find the probability that their mean weight is between 120 lb and 161 lb. The probability is approximately ______. ​(Round to four decimal places as​ needed.)

c. When redesigning the ejection​ seat, which probability is more​ relevant?
A. Part​ (a) because the seat performance for a single pilot is more important.
  B. Part​ (b) because the seat performance for a sample of pilots is more important.
C. Part​ (a) because the seat performance for a sample of pilots is more important.
  D. Part​ (b) because the seat performance for a single pilot is more important.

Question 4. An engineering firm is constructing power plants at three different sites. Define the events E1, E2, E3 as follows:
E1 = the plant at site 1 is completed by the contract date
E2 = the plant at site 2 is completed by the contract date

E3 = the plant at site 3 is completed by the contract date
An extensive analysis of the history of the performance of this firm has estimated the following probabilities for each of these events:
P(E1) = 0.85
P(E2) = 0.90
P(E3) = 0.75
Given that E1 is completed, P(E3) is 0.8
The probability all three are completed on time is 0.66
The probability no plants are completed on time is 0.03
The probability that both E1 and E2 are completed on time is 0.80
The probability that only E2 is completed on time is 0.05

For each scenario (event) described below (b-g), draw a new Venn diagram that shades the area of interest, write the event using proper set notation, and determine the associated probability.

f) Exactly one of the three plants is completed by the contract date

1) The table below shows how many people out of customers of a shop were young or adult and make or
did not make a purchase.

a) (5 pts) Find the probability the random consumer is young if he/she made a purchase. Round the
decimal
answer to 3 decimal places.
?(? ?? ??) =

b) (2 pts) Find the probability the random consumer is young. Round the decimal answer to 3 decimal
places.
?(?) =

c) (2 pts) Find the probability the random consumer did not make a purchase. Round the decimal
answer to 3
decimal places.
?(??) =

d) (2 pts) Find the probability the random consumer is adult and did not make a purchase. Round the
decimal
answer to 3 decimal places.
?(? ??? ??) =

e) (5 pts) Find the probability the random consumer is either young or did not make a purchase.
Round the
decimal answer to 3 decimal places.
?(? ?? ??) =

An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 150 lb and 191 lb. The new population of pilots has normally distributed weights with a mean of 156 lb and a standard deviation of 29.1 lb.

A. If a pilot is randomly​ selected, find the probability that his weight is between 150 lb and 191 lb.

The probability is approximately_______?

​(Round to four decimal places as​ needed.)

B. If 38 different pilots are randomly​ selected, find the probability that their mean weight is between 150 lb and 191 lb.

The probability is approximately_______?

​(Round to four decimal places as​ needed.)

C.When redesigning the ejection​ seat, which probability is more​ relevant?

A.Part​ (a) because the seat performance for a sample of pilots is more important.

B.Part​ (b) because the seat performance for a single pilot is more important.

C.Part​ (b) because the seat performance for a sample of pilots is more important.

D.Part​ (a) because the seat performance for a single pilot is more important.

Question I
In the senior year of a high school graduating class of 100 students, 42 studied mathematics, 68 studied psychology, 54 studied history, 22 studied both mathematics and history, 25 studied both mathematics and psychology, 7 studied history but neither mathematics nor psychology, 10 studied all three subjects, and 8 did not take any of the three. Randomly select a student from the class and find the probabilities of the following events.
(a) A person enrolled in psychology takes all three subjects.
(b) A person not taking psychology is taking both history and mathematics

A
The probability that an automobile being filled with gasoline also needs an oil change is 0.25; the probability that it needs a new oil filter is 0.40; and the probability that both the oil and the filter need changing is 0.14.
(a) If the oil has to be changed, what is the probability that a new oil filter is needed?
(b) If a new oil filter is needed, what is the probability that the oil has to be changed?

A: Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.)
P(z ≤ 1.23) =

B: Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.)

P(z ≥ −1.13) =

C: Let z be a random variable with a standard normal distribution. Find the indicated probability. (Round your answer to four decimal places.)

P(−1.87 ≤ z ≤ −1.24) =

D: Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)

μ = 42; σ = 15

P(50 ≤ x ≤ 70) =

E: Assume that x has a normal distribution with the specified mean and standard deviation. Find the indicated probability. (Round your answer to four decimal places.)

μ = 108; σ = 18

P(x ≥ 90) =

A company manufactures computers, whose hard disk has a capacity of 20 GB and others of 30 GB. In the previous month, 35% of the computers sold were those with a 20 GB hard drive. Of buyers of computers with a 20 GB hard drive, 45% buy those with 356 MB of RAM, while 30% of buyers of computers with a 30 GB hard drive also do so.
(a) What is the probability that a randomly selected computer will have a 20 GB hard drive and 356 MB RAM?
(b) What is the probability that 5 of 23 randomly selected computers have a 20GB hard drive and 356MB RAM?
(c) What is the probability that the randomly selected computer has a 30 GB hard drive and 356 MB RAM?
(d) What is the probability that 7 out of 23 randomly selected computers have a 30 GB hard drive and 356 MB RAM?
(e) What is the probability that exactly 6 out of 23 randomly selected computers have 356 MB of RAM?

A dishwasher has a mean lifetime of 12 years with an estimated standard deviation of 1.25 years. Assume the lifetime of a dishwasher is normally distributed. Round the probabilities to four decimal places. It is possible with rounding for a probability to be 0.0000.

a) State the random variable. rv X = the lifetime of a randomly selected dishwasher Correct

b) Find the probability that a randomly selected dishwasher has a lifetime of 8.25 years or more.

c) Find the probability that a randomly selected dishwasher has a lifetime of 12.25 years or less.

d) Find the probability that a randomly selected dishwasher has a lifetime between 8.25 and 12.25 years.

e) Find the probability that randomly selected dishwasher has a lifetime that is at most 8.875 years.

f) Is a lifetime of 8.875 years unusually low for a randomly selected dishwasher? Why or why not? Select an answer

g) What lifetime do 58% of all dishwashers have less than? Round your answer to two decimal places in the first box. Put the correct units in the second box.

Now suppose that one of the 50 states is selected at random, so each state has a 1/50 = .02 probability of being selected.

1. Determine the conditional probability that A has visited the (randomly selected) state, given that the state lies to the west of the Mississippi River. Then determine this conditional probability, given that the state lies to the east. Comment on how these conditional probabilities compare, and what that means in this context.

2. Is whether or not person A visited a state independent of whether the state lies to the east or west of the Mississippi River? Justify your answer.

3. Determine the conditional probability that the (randomly selected) state lies to the west of the Mississippi River, given that A or B has visited the state.

4. Determine the conditional probability that the (randomly selected) state lies to the west of the Mississippi River, given that A and B have visited the state.

According to a study done by De Anza students, the height for Asian adult males is normally distributed with an average of 66 inches and a standard deviation of 2.5 inches. Suppose one Asian adult male is randomly chosen. Let X = height of the individual.

Part B.

Find the probability that the person is between 64 and 69 inches.

Write the probability statement.

What is the probability? (Round your answer to four decimal places.)

Sketch the graph.

Part C.

Would you expect to meet many Asian adult males over 74 inches? Explain why or why not, and justify your answer numerically.

---Select--- Yes No , because the probability that an Asian male is over 74 inches tall is.

Part D.

The middle 40% of heights fall between what two values?

Write the probability statement.

P(x₁ < X < x₂) =

State the two values. (Round your answers to one decimal place.)

Sketch the graph.