A random variable has a triangular probability density function with a = 50, b = 375, and m = 250.

What is the probability that the random variable will assume a value between 70 and 250? If required, round your answer to four decimal places.

Every day of spring the probability that a thunderstorm takes place in Toronto is 0,005. We assume that the events are independent and that the spring starts March 21st.

1) What is the probability that the third storm takes place May 1st?

2) What is the probability that the third storm takes place May 1st knowing that it is April 15th and a storm has just occurred the first time this Spring?

You are given an unfair coin (the probability of heads is 1/3) and decide to toss it ten times. Following Example 5.3 in your textbook, plot the binomial probability mas function for N = 10 and p = 1/3. What is the probability that the coin will come up heads 5 times in 10 tosses?

Determine the mean, variance, and joint second moments.

a. Y = cos

1. According to a study, 20% of corporate officers at public-held companies are women. Suppose that you select a random sample of 250 corporate officers.
   1. What is the probability that in the sample, less than 15% of the corporate officers will be women?
   2. What is the probability that in the sample, between 13% and 17% of the corporate officers will be women?
   3. What is the probability that in the sample between 10% and 20% of the corporate officers will be women?

1. A certain type of pump’s time until failure has an exponential distribution with a mean of 5000 hours. State answers rounded to two decimal places.
   1. What is the probability it will still be operating after 3000 hours of service?
   2. What is the probability that it will fail prior to 6000 hours of service?
   3. If it has been running for 3000 hours, what is the probability it will still be running 2000 hours later?

Amazon's third-largest market is the United Kingdom. In 2019, the employees at a local firm in London received their salary and decided to spend a portion of it on making online purchases from Amazon. The probability that the online purchases will be shipped on time to each employee is 0.68. Determine the following:

a. The probability that three products will be shipped on time.

b. The probability that out of three, two products will be shipped on time.

describe an example that uses discrete probabilities or distributions. Provide an example that follows either the binomial probabilities or any discrete probability distribution, and explain why that example follows that distribution. In your responses to other students, make up numbers for the example provided by that other student, and ask a related probability question. Then show the work (or describe the technology steps) and solve that probability example.

Given a population with a mean of μ= 103 and a variance of σ² = 16, the central limit applies when the sample size n >_25. A random sample of size n = 25 is obtained.

a. What are the mean and variance of the sampling distribution for the sample means?

b. What is the probability that X^{- >} 104 ?

c. Whta is the probability that 102 < X < 104 ?

d. What is the probability that X^- <_ 103.5 ?

A project completion time can be assumed to be represented by a normal distribution curve The project is expected to complete in 36 weeks with a path variance of 6.67 Base on the information provided, calculate: a. Calculate the probability that the project will be completed in 39 weeks or less b. The probability that the project will be completed in between 33.5 and 38 weeks c. With 95 percent probability, calculate the date the project can be completed.