Bana 2081 Exam 2 Questions with Correct
Answers
The random variable x is known to be uniformly distributed between 1.0 and 1.5.
A) Show the graph of the probability density function.
B) Compute P(x = 1.25).
C) Compute P(1.0 ≤ x ≤ 1.25).
D) Compute P(1.2 < x < 1.5).
A) f(x) axis 2, X axis 1.5
B) 0
C) 2(0.25) = 0.50
D) 2(0.30) = 0.60
Delta Airlines quotes a flight time of 5 hours, 3 minutes for a particular flight. Suppose
we believe that actual flight times are uniformly distributed between 5 hours and 5
hours, 12 minutes.
A) Show the graph of the probability density function for flight time.
B) What is the probability that the flight will be no more than 3 minutes late?
C) What is the probability that the flight will be more than 6 minutes late?
D) What is the expected flight time, in minutes?
A) Y axis is (1/12) X axis is 300-312
B) (1/12)(306 − 300) = 0.5
C) (1/12)(312 − 309) = 0.25
D)(300 + 312)/2 = 306
Most computer languages include a function that can be used to generate random
numbers. In Excel, the RAND function can be used to generate random numbers
, between 0 and 1. If we let x denote a random number generated using RAND, then x is
a continuous random variable with the following probability density function.
f(x) =
1 for 0 ≤ x ≤ 1
0 elsewhere
A) Graph the probability density function.
B) What is the probability of generating a random number between 0.15 and 0.65?
C) What is the probability of generating a random number with a value less than or
equal to 0.30?
D) What is the probability of generating a random number with a value greater than
0.80?
A) y axis 1 x axis 1
B) 1(0.50) = 0.50
C) 1(0.30) = 0.30
D) 1(0.20) = 0.20
A random variable is normally distributed with a mean of
μ = 50
and a standard deviation of
σ = 5.
A) The following figure shows that the normal curve almost touches the horizontal axis
at three standard deviations below and at three standard deviations above the mean (in
this case at 35 and 65).
B) What is the probability the random variable will assume a value between 40 and 60?
Answers
The random variable x is known to be uniformly distributed between 1.0 and 1.5.
A) Show the graph of the probability density function.
B) Compute P(x = 1.25).
C) Compute P(1.0 ≤ x ≤ 1.25).
D) Compute P(1.2 < x < 1.5).
A) f(x) axis 2, X axis 1.5
B) 0
C) 2(0.25) = 0.50
D) 2(0.30) = 0.60
Delta Airlines quotes a flight time of 5 hours, 3 minutes for a particular flight. Suppose
we believe that actual flight times are uniformly distributed between 5 hours and 5
hours, 12 minutes.
A) Show the graph of the probability density function for flight time.
B) What is the probability that the flight will be no more than 3 minutes late?
C) What is the probability that the flight will be more than 6 minutes late?
D) What is the expected flight time, in minutes?
A) Y axis is (1/12) X axis is 300-312
B) (1/12)(306 − 300) = 0.5
C) (1/12)(312 − 309) = 0.25
D)(300 + 312)/2 = 306
Most computer languages include a function that can be used to generate random
numbers. In Excel, the RAND function can be used to generate random numbers
, between 0 and 1. If we let x denote a random number generated using RAND, then x is
a continuous random variable with the following probability density function.
f(x) =
1 for 0 ≤ x ≤ 1
0 elsewhere
A) Graph the probability density function.
B) What is the probability of generating a random number between 0.15 and 0.65?
C) What is the probability of generating a random number with a value less than or
equal to 0.30?
D) What is the probability of generating a random number with a value greater than
0.80?
A) y axis 1 x axis 1
B) 1(0.50) = 0.50
C) 1(0.30) = 0.30
D) 1(0.20) = 0.20
A random variable is normally distributed with a mean of
μ = 50
and a standard deviation of
σ = 5.
A) The following figure shows that the normal curve almost touches the horizontal axis
at three standard deviations below and at three standard deviations above the mean (in
this case at 35 and 65).
B) What is the probability the random variable will assume a value between 40 and 60?
