Uniform, Normal and Exponential Distributions and Conditional Probability

1. The length of time it takes to find a parking spot, during the summer terms on a campus, follows a normal distribution with a mean of 3.5 minutes and a standard deviation of 1 minute. The probability that a student, attending classes during the summer terms, will find a parking spot in less than 3 minutes is

2. Suppose that a class in elementary statistics was allocated 15 minutes to complete a quiz. It can be assumed that the time X it takes to complete the quiz is uniformly distributed over the interval [0, 15]. Suppose a student from the class is selected at random, what is the probability that the student will take more than 10 minutes to complete the quiz?

3. The defective rate for a certain electronic component is known to be 6%. If 100 of the components are selected at random, what is the probability that less than 10 are defective?

4. A rock crushing company has three plants, all receiving blasted rocks in bulk. The amount of rocks that can be crushed by one of the plants in one day can be modeled by an exponential distribution. The mean amount of rocks that can be crushed per day by each plant is 4 tons. Assume that the plants operate independently of each other. What is the probability that two of the plants will crush more than 4 tons on a given day?

5. Suppose that the life of an electronic component has an exponential distribution with a mean life of 500 hours. Suppose that the component was in operation for 400 hours. What is the conditional probability that it will last another 500 hours?

6. Suppose that an e-business on the Internet receives an average of 5 orders per hour. Assume that the number of orders follows a Poisson process. What is the probability that up to one hour will elapse until two orders are received?

Uniform, Normal and Exponential Distributions and Conditional Probability are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

X~N(500,400) Determine the following
Random Variable X
a) P( X <= 515 )
b) P( X <= 515 | X > 450 ) (note: "|" implies given)
c) P( 20 < X^(1/2) <= 25 ) ( i.e. 20 < "square root of X" < 25 )
please clearly state each step for each part. The attached file states the problem again.

1. The useful life of an electrical component is exponentially distrbuted with a mean of 2500 hours.
(a) what is the probability the circuit will last more than 3000 hrs.
(b) what is the probability the circuit will last between 2500 and 2750 hours
(c ) what is the probability the circuit will fail within the first 2000 hr

What is an important difference between the uniform andnormalprobabilitydistributions?
The mean, median and mode are all equal .
The mean and median are equal
They are negatively skewed
About 68% of all observations are within one standard deviation of the mean.

You arrive at a bus stop at 10 o'clock, knowing that the bus will arrive at some time uniformly distributed between 10:00 and 11:00.
a) What is the probability that you will have to wait longer than 10 minutes?
b) If at 10:20 the bus has not arrived, what is the probability that you will have to wait atleast an additional 10 m

A. Simulate 50 observations from a normal distribution with mean 0 and standard deviation 1. make a normal plot.
b. Repeat the simulation of (a) but use an exponential distribution with mean = 1 how does the shape of the plot compare to the plot using normal data?
c. Repeat the simulation in (a) but use a uniform distribu

A) A fire station is to be located along a road of length A, A<∞. If fires will occur at points uniformly chosen of (0, A), where should the station be located so as to minimize the expected distance from the fire? That is, choose a so as to
minimize E[|X-a|] when X is uniformly distributed over (0,A).
b) N

QUESTION 1
A continuous uniform distribution U(100,200) will have the same standard deviation as a continuous uniform distribution U(200,300).
True
False
QUESTION 2
There is a simple formula for normal areas, but we prefer a table for greater accuracy.
True
False
QUESTION 3
The area under a normal curve is 1 onl

Determine the value of c that makes the function f(x,y) = c(x+y) a joint probability density function over the range:
x greater than 0 and less than 3 and x less than y less than x+2
a) P(X<1, Y<2)
b) P(11)
d) P(X<2, Y<2)
e) E(X)
f) V(X)
g) Marginal probability distribution of X
h) Conditional probabilit

The one-mile running time for CMS male athletes is approx. distributed normally with a mean of 7.5 minutes and a standard deviation of 0.6 mins. (A) What percentage of athletes run a mile in less than 7 minutes? In less than 8 mins? In more than 6.5? Between 7 and 8 mins? (B) If a male athlete is randomly chosen, what is the

A class consist of 10 males and 30 females. If one student is randomly selected from the class what is the probability of selecting a male?
- 1/40
- 1/10
- 10/30
- 10/40
A class consist of 10 males and 30 females. a random sample of n=3 is selected. If the first two students are both females what is the probability that t