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 with 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)