STA301 Statistics and Probability Assignment 2 Solution Spring 25th June 2013

Assignment No: 2 (Lessons 28-30)

Question 1:                                                                                                                   Marks: 4+4=8a)  Suppose 4 dresses are randomly chosen without replacement from the total of 8 dresses (5 red and 3 white). Calculate the probability of getting exactly 2 red dresses out of 5 red dresses. (Solve using hypergeometric distribution)a) 43% (consider revising)b)   A random variable “X” following binomial distribution with n=5 and p=0.5 Calculate the mean, variance and Coefficient of Variance.

Solution:

1. mean: 2.5
2. variance: 1.25
3. coefficient of variance: 1.12

Question 2:                                                                                                                   Marks: 4+3=7

a)  One hundred passengers have made reservations for a train. If the probability that a passenger who has a reservation will not show up is 0.01, what is the probability that exactly 2 will not show up? (Use appropriate distribution)
 a) 0.1839 i.e. 18.39% (Poisson distribution)
b)  A certain type of car battery lasts on an average 2 years, with a standard deviation    of 0.5 year. Assuming that the battery lives are normally distributed, find the probability that a given battery will last less than 2.5 years.
b) 15.87% (consider revising)