5. Length of employment at a certain firm seems to be a normal random variable w
ID: 3340860 • Letter: 5
Question
5. Length of employment at a certain firm seems to be a normal random variable with mean µ = 11 years and a standard deviation of = 5 years.
(a) What proportion of people make it to 10 years?
(b) What proportion of people leave in the first three years?
(c) If 200 people start this year, what is the probable number of them that will still be there after 7 years?
6. Ten students take a test and the scores are {80, 99, 83, 82, 100, 75, 83, 85, 71, 92}.
(a) Compute the sample mean and sample standard deviation.
(b) Let X represent the normal random variable whose mean is the sample mean and whose standard deviation is the sample standard deviation. What is P (X > 90)? What proportion of students actually did score above a 90?
(c) If an A is given to any student whose score is greater than 1 standard deviation above the mean (using normal with sample mean and sample deviation), how many students get an A?
(d) If a normal random variable with mean 80 and standard deviation 10 is used, how many students get an A (more than 1 standard deviation away from the mean)?
Explanation / Answer
the PDF of normal distribution is = 1/ * 2 * e ^ -(x-u)^2/ 2^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd ~ N(0,1)
mean ( u ) = 11
standard Deviation ( sd )= 5
a.
P(X < 10) = (10-11)/5
= -1/5= -0.2
= P ( Z <-0.2) From Standard Normal Table
= 0.4207
42.07% are make it 10 years
b.
P(X < 3) = (3-11)/5
= -8/5= -1.6
= P ( Z <-1.6) From Standard Normal Table
= 0.0548
5.38% are leave in first 3 years
c.
P(X > 7) = (7-11)/5
= -4/5 = -0.8
= P ( Z >-0.8) From Standard Normal Table
= 0.7881
78.81% will still be there after 7 years
n = 200
expected people = np = 200 * 0.7881 = 157.62 ~ 158
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.