MGMT2262
Worksheet #4
1) Suppose the amount of paint that goes into a 4 L can is uniformly distributed between 3.85 L and 4.15 L.
a) What is the probability a can has less than 3.9 L? (16.67%)
b) What is the probability a can has more than 4.05 L? (33.33%)
c) Suppose the company wants the amount of paint in a can to be within 0.5 standard deviations of the mean. Based on the probability of this happening, are these realistic expectations? (28.87%; no)
2)
A
convenience store averages 2 customers per minute.
a) What is the probability that it will go more than 2 minutes between customers? (1.83%)
b) What is the probability that it will go less than 1 minute between customers? (86.47%)
3)
Suppose
that when there are 6 tellers on hand, a bank serves 1 customer per minute on
average.
a) Suppose that when I go to the bank, there are 6 tellers and there are 10 people in front of me. What is the probability I will wait more than 10 minutes? (36.79%)
b) Suppose there are only 3 tellers and there are 10 people in front of me. What is the probability I will wait more than 10 minutes? (60.65%)
c) Suppose there are 4 tellers and there are 8 people in front of me. What is the probability I will wait more than 15 minutes in total if I’ve been waiting 10 minutes already? (65.92%)
4)
Find
the following:
a)
P(0
< Z < 1.58) (0.4429)
b)
P(-3.2
< Z < 0) (0.4993)
c)
P(-1.28
< Z < 0.67) (0.6483)
d)
P(1.39
< Z < 2.54) (0.0768)
e)
P(-1.98
< Z < -0.02) (0.4681)
f)
The
85.08th percentile of Z (1.04)
g)
The
value of x such that P(-x < Z < x) = 0.9756 (2.25)
5)
Suppose
X is normally distributed with a mean of 5 and a standard deviation of 2. Find
the following:
a)
P(X
< 7) (0.8413)
b)
P(X
> 9.2) (0.0179)
c)
P(4
< X < 6.4) (0.4495)
d)
The
93.7th percentile (8.06)
e)
The
two values between which 95.44% of the distribution lies (1 and 9)
6)
Suppose
the amount of monthly disposable income people have is normally distributed
with a mean of $800 and a standard deviation of $75.
a)
What
is the probability someone has a monthly disposable income of less than $750?
(0.2514)
b)
What
is the probability someone has a monthly disposable income of more than $900?
(0.0918)
c)
What
is the cutoff for the top 5% of monthly disposable incomes? ($923.38)
d)
Between
which two values would 79.6% of monthly disposable incomes lie? ($704.75 and
$895.25)
7)
Suppose
the running time for the 100m dash is normally distributed with a mean of 10.2
seconds and a standard deviation of 0.2 seconds.
a)
What
is the probability a runner’s time is under 10.01
seconds? (0.1711)
b)
What
is the probability a runner’s time is over 10.3 seconds? (0.3085)
c)
What
is the cutoff time for a runner to place in the fastest 5%? (9.871 seconds)
d)
Between
which two values would 99.7% of the distribution lie, based on the empirical
rule? (9.6 and 10.8)
From the textbook
5.9 (page
150)
5.29 (page
164)
5.57 (page
172)
6.13 (page
192)