Question

Poisson

1. Passengers of the areas lines arrive at random and independently to the documentation section at the airport, the average frequency of arrivals is 1.0 passenger per minute.

to. What is the probability of non-arrivals in a one minute interval?

b. What is the probability that three or fewer passengers arrive at an interval of one minute?

C. What is the probability not arrived in a 30 second interval?

d. What is the probability that three or fewer passengers arrive in an interval of 30 seconds?

2. The average number of spots per yard of fabric follows a Poisson distribution. If λ = 0.2 spot per square yard.

to. Determine the probability of finding 3 spots in 2 square yards.

b. What is the probability of finding more than two spots in 4 square yards?

C. What is the average stain in 10 square yards?

Hypergeometric

1. It is known that of 1000 units of ACME cars of a lot of 8000, they are red. If 400 cars were sent to a wholesaler, what is the probability that you will receive a hundred or less red cars. (Assume X = red auto)

a) P (X <= 100) =? (Hypergeometric)

b) P (X> 50) =?

c) E (x) = expected value red cars

I. Continuous Distribution: Normal

1. Long distance telephone calls have a normal distribution with µ x = 8 minutes and σx = 2 minutes. Taking a unit up.

to. What is the probability that a call will last between 4 minutes and 10 minutes?

b. What is the probability that a call will last less than 9 minutes?

C. What is the value of X so that 12% of the experiment values ​​are greater than it?

d. If samples of size 64 are taken:

i. What proportion or probability of the sample means of the calls will be between 7 minutes and 9 minutes?

ii. What proportion or probability of the sample means of the calls is greater than 5 minutes?

iii. Between that two values ​​from the sample mean are 90% of the data.

Exponential

1. The time to fail in hours of a laser beam in a cytometric machina can be modeled by an exponential distribution with λ = .0005

to. What is the probability that a laser will fail more than 10000 hours?

b. What is the probability that a laser will fail less than 20,000 hours?

C. What is the probability that a laser will fail between 10,000 and 20,000 hours?

Answer 1

Answer:

1.

a)

Here we use poisson distribution

= 1

Probability = P(X = 0)

= e^-*^x/x!

= e^-1*1^0/0!

= 0.3679

P(X = 0) = 0.3679

b)

Now P(X <= 3) = e^-*^x/x!

= e^-1*1^0/0! + e^-1*1^1/1! + e^-1*1^2/2! + e^-1*1^3/3!

= 0.9810

P(X <= 3) = 0.9810

c)

Here = 30 seconds

= 1/2

= 0.5

P(X = 0) = e^-*^x/x!

= e^-0.5*0.5^0/0!

= 0.6065

P(X = 0) = 0.6065

d)

Now P(X = 3)

= e^-*^x/x!

So now on solving we get

= 0.9982

P(X = 3) = 0.9982

I hope it works for you.

Please post as separate questions as well as post. Thank you.