Please do question 5 Problem 3 10 points Assume that a test

Please do question 5 .

Problem, 3. (10 points) Assume that a test for a particular disease comes back positive 99% of the time if the person has the disease and comes back negative 95% of the time if the person does not have the disease. It is known that 1.190 percent of the tests were positive. Estimate the prevalence of the disease in the population and comment. Problem 4. (10 points) There are m men and n women applying for 2k jobs (min(m,n) -2k) at a company. Assume that all applicants are equally qualified. a) Find the probability that all jobs are given to women only. a particular pair of applicants will be hired. Problem 5. (10 points) A magazine has a set limit of 3500 on the word count of its articles. The editor has noticed that the articles sent for publication are consistently over the limit and she estimated that the distribution of the word counts is N(3900,02) a) Find 2 if only 10% ofthe submitted articles meet the word limit of 3500. b) Determine what the word limit should be if we want 75% of the submitted articles to meet it. c) What is the proportion of submitted articles with word counts between 3500 and 3900? -kry2 and oxy2 and Problem 6. (10 points) Let X and Y be continuous random variables with joint pdf f(x, y) support set 0

Solution

a).

from standard normal distribution, P( z <-1.282) = 0.10

z=( x-mean)/sd

Therefore (3500-3900)/sd =-1.2816

-400/ -1.2816 = sd

Sd=312.1099

Variance =97412.60

b).

from standard normal distribution, P( z < 0.674) = 0.75

x =3900+0.674*312.1099 = 4110.36

the required word limit =4110

c).

z value for 3500, z=(3500-3900)/312.1099= -1.2816

z value for 3900, z=(3900-3900)/312.1099 = 0

P( 3500< x<3900) =P( -1.2816<z <0)

P( z <0) – P( z < -1.2816)

=0.50 - 0.10

= 0.40