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Chapter 5 Homework
Question 1: Which type of distribution does the graph illustrate?
Uniform distribution.
Question 2: Which type of distribution does the graph illustrate?
Exponential distribution
Question 3: which type of distribution does the graph illustrate?
Normal distribution
Question 17: In this distribution, outcomes are equally likely. What does it mean?
This means that the value of x is likely to be any number between 1.5 and 4.5
Question 18: What is the height of f(x) for continuous probability distribution?
𝑋~𝜇 (1.5, 4.5)
F(x)= 1/ (b-a) for a 𝑋~𝜇 (1.5, 4.5)
F(x) = 1/ (4.5 -1.5)
F(x) = 0.333
Question 19: What are the constraints for the values of x?
1.5 ≤ 𝑥 ≤ 4.5
Question 25: Find the probability that a randomly selected home has more than
3,000 square feet given that you already know the house has more than 2,000
square feet.
𝑋~𝜇 (1.5, 4.5)
F(x) = 1/ (4.5- 2) =1/2.5 for 2< x< 4.5
P(x> 3| x> 2) = (4.5 – 3) (1/2.5)
= 0.6
Question 29: what is the theoretical mean?
Theoretical mean = 6
Question 34: what is being measured here?
Age of cars in years
Question 46: What type of distribution is this?
Exponential distribution
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Question 58: What is the cumulative distribution function?
Is the probability function the x takes; in this case cdf = 0.75
Question 64: what is being measured here?
The period (in years) it will take to decay carbon-14
Question 65: Are the data discrete or continuous?
continuous
Question 66: In words, define the random variable X
Random variable x is a numerical description of the outcome of a statistical
experiment.
Question 67: what is the decay rate (m)?
m = 0.000121
Question 73: When age is rounded to the nearest year, do the data stay
continuous, or do they become discrete? Why?
Age is a discrete regardless of the accuracy of rounding off
Question 81: The probability of waiting more than seven minutes given a person
has waited more than four minutes is
P(x> 7| x>4)
1/ (8-4) = ¼
Probability is 0.25
Question 83: Suppose that the value of a stock varies each day from $16 to $25
with a uniform distribution
a) Find the probability that the value of the stock is more than $19
F(x) = (1/ 25 – 1/16)
F(x) = 1/9
P(x> 19) = (25 – 19) (1/9) = 2/3
b) Probability between $19 and $ 22
P (19 < x < 22)
= (22 – 19) (1/9) = 1/3
c) The upper quartile 25%
25% = 0.25
0.25=x(1/9)
X= (0.25)(9)
= 2.25
Quartile = 25 – 2.25
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Quartile = 22.75
d) Given stock is greater than $18 find the probability the stock is more than
$21
P(x> 21| x> 18)
F(x) = 1/ 21 – 1/18 = 1/7
P(x> 21| x> 18) = (25 – 21) 1/7
P(x> 21| x> 18) = 4/7
Question 92: What is the probability that a phone will fail two years of the date
of purchase
P(2<x<3)
P (x>2) = 1- (1 -e^ (0.333*2))
= 0.5137
Question 100:
a) Find the probability that the duration between two successive visits to the
website is more than ten minutes
P(T< t)= 1 – e^(t/60)
= 1 – e^ (-1/6)
=1- 0.8464
= 0.154
b) The top 25% of durations between visits are at least how long?
25% = 0.25
P(T<t) = 0.25
0.25 = 1 – 163/t
T = 122 minutes
c) Suppose that 20 minutes have passed since the last visit to the website.
What is the probability that the next visit will occur within the next 5
minutes?
P(T> 20| T> 5)
P(T> 5) = 1 – (1- e^ -(5/60)
=0.92
d) Find the probability that less than 7 visits occur within a one-hour period?
P (X< 7)
= 1 – (1- e^ (-7/60)
= 0.8898
