Let N be a random variable defined as the number of days of paid vacation for people in the U.S. Let's suppose a statistician comes up with the following probability function for N: fN(n)={0.15 for n=0,0.15 for n=5,0.35 for n=8,0.1 for n=10, and 0.25 for n=12}. What is the expected value of N? Give your answer as a decimal.

В2. (a) Given the probability Venn diagram below for the two Events A and B find the probabilities: 0.6 0.5 A 0.2 (i) (ii) (iii) Pr( A 'OR' B) Pr( Not-A 'AND' Not-B) Pr( Not-A "OR' Not-B) (b) A random sample from a population of X with unknown mean but a known variance, o = 400, gives the following data: sample size, n= 125, Ex= 1750. (i) Give a point estimate of the population mean, u. (ii) Is this estimate biased or not. Give a reason. (ii) Derive a 95% confidence interval for the population mean, µ.

Suppose a random variable x is best described by a uniform probability distribution with range 0 to 5. Find the value of a that makes the following probability statements true.

The taxi and takeoff time for commercial jets is a random variable x with a mean of 8.3 minutes and a standard deviation of 2.5minutes. Assume that the distribution of taxi and takeoff times is approximately normal. You may assume that the jets are lined up on a runway so that one taxies and takes off immediately after the other, and that they take off one at a time on a given runway.   (a) What is the probability that for 36 jets on a given runway, total taxi and takeoff time will be less than 320 minutes? (Round your answer to four decimal places.)(b) What is the probability that for 36 jets on a given runway, total taxi and takeoff time will be more than 275 minutes? (Round your answer to four decimal places.)(c) What is the probability that for 36 jets on a given runway, total taxi and takeoff time will be between 275 and 320 minutes? (Round your answer to four decimal places.)

The president of Doerman Distributors, Inc., believes that 28% of the firm's orders come from first-time customers. A simple random sample of 100 orders will be used to estimate the proportion of first-time customers.  What is the probability that the sample proportion will be between 0.16 and 0.40 (to 4 decimals)? What is the probability that the sample proportion will be between 0.21 and 0.35 (to 4 decimals)?

The number of automobile sold weekly at a certain dealership is a random variable with expected value 16.Give an upper bound to the probability that the next week sales exceed 18.

Outside the airport terminal, at the shuttle stop, you sometimes wait a long time for the right shuttle that will take you to your hotel.

There is a bus coming to a bus stop every 10 minutes. The waiting time of any person at the stop is a random variable with a continuous uniform distribution. What is the probability that the waiting time is at most two minutes?

Let X be a chi-squared random variable with 12 degrees of freedom. What is the probability that X is greater than 23? What are the steps to come to this conclusion?

Fawns between 1 and 5 months old in Mesa Verde National Park have a body weight that is approximately normally distributed 25.36 kg and standard deviation q = 4.72 kg. Let x be the weight of a fawn in kg. What is the probability that for a fawn chosen at random: with mean u - (a) x is less than 28.88 kg? (b) x is greater than 17.34 kg? (c) x lies between 29.04 and 33.6 kg? -