a) The following Table lists the probability distribution of a discrete random variable x: 1 2 4| 5 Р(x) | 0.19 0.32 0.24 * 0.06 0.03 (i) Calculate the expected value (mean), variance and the standard deviation of the probability distribution. b) Eighty percent (80%) of lecturers will be able to obtain a parking space at a university car park. If there are 275 lecturers with vehicles on campus each day, what is the probability that at least 215 lecturers will obtain a parking space on a given day? Use a suitable approximation in your response.

2. If Z is a standard normal variable, find the following probabilities:a) P (Z < - 0.43) =b) P (- 0.43 < Z < 1.28) =c) P (Z > - 0.28) =

A random sample of 3 households is selected. The probabilities that certain number of households have a pet dog are listed. prob. of households with a dog P(x) probability that x households have %3D x (# of households) a dog 0.036 1 0.219 2 0.444 0.301 a) Does this table describe a probability distribution? Give a reason for your answer. Do not simply say yes/no b) What is the mean? Show work Edit View Insert Format Tools Table BIUA e Pv: 12pt v Paragraph v DELL

1. Consider the following probability distribution for the continuous random variable, X. 1 حا 4 5 X a. Find P(2 < X<4) (4-2) 4-10.9= 0.5 b. Find P(4 < X <5) 50.25 6= 0.25 c. Find P(X<4) -3.0