Question

If the customers purchasing laptops, 75% purchase a

Dell model. Let X= the number among the next 5

purchasers who select the Dell model.

a) What is the pdf of X?

b) Compute P(X > 4) and P(2 £ X < 4).

c) Compute the mean and the variance of X.

Answer #1

Of all customers purchasing automatic garage-door openers, 75%
purchase a chain-driven model. Let X = the number among
the next 15 purchasers who select the chain-driven model.
(a) What is the pmf of X?
a) h(x; 3, 15, 75)
b) nb(x; 15, 0.25)
c) b(x; 15, 0.25)
d) h(x; 12, 15, 75)
e) nb(x; 15, 0.75)
f) b(x; 15, 0.75)
(b)
Compute P(X > 10).(Round
your answer to three decimal places.)
P(X > 10) =
(c) ComputeP(7 ≤ X ≤...

Of all customers purchasing automatic garage-door openers, 60%
purchase a chain-driven model. Let X = the number among
the next 15 purchasers who select the chain-driven model.
(a)
What is the pmf of X?
b(x; 15, 0.4)
nb(x; 15, 0.6)
h(x; 9, 15, 60)
b(x; 15, 0.6)
h(x; 6, 15, 60)
nb(x; 15, 0.4)
(b)
Compute
P(X > 11).
(Round your answer to three decimal places.)
P(X > 11) =
(c)
Compute
P(7 ≤ X ≤ 11).
(Round your...

Of all customers purchasing automatic washer, 75% purchase a
Samsung model. If a store currently has in stock 10 Samsung models
and 8 Haier models washers, what is the probability that the
requests of the next 10 customers for a Samsung model can all be
met from existing stock?

The number of customers who make a purchase using a credit card
at H&M has the following distribution where X = number of
customers who use a credit card to make a purchase
X
0
1
2
3
4
p(X)
0.03
0.17
0.37
0.33
0.10
(It may be helpful to copy the numbers into Excel for faster
calculations)
(Round all answers to two decimal places)
a) What is the probability that at least one but no more than
three customers...

For customers purchasing a refrigerator at a certain appliance
store, let A be the event that the refrigerator was
manufactured in the U.S., B be the event that the
refrigerator had an icemaker, and C be the event that the
customer purchased an extended warranty. Relevant probabilities are
below.
P(A) = 0.74
P(B | A) =
0.95
P(B | A' ) = 0.77
P(C | A ∩ B) =
0.84
P(C | A ∩ B' )
= 0.55
P(C |...

A small store keeps track of the number X of customers
that make a purchase during the first hour that the store is open
each day. Based on the records, X has the following
probability distribution.
X
0
1
2
3
4
P(X)
0.1
0.1
0.1
0.6
Determine P(x=2):
Determine P(x≥3):
Determine P(x<3):
Determine the mean number of customers:
Determine the standard deviation of the number of customers

Customers at a gas station pay with a credit card (A),
debit card (B), or cash (C). Assume that
successive customers make independent choices with
P(A) = 0.5, P(B) = 0.3,and
P(C) = 0.2.
(a) Among the next 100 customers, what are the mean and variance
of the number who pay with a debit card?
mean
customers
variance
customers2
Explain your reasoning.
Because we are interested in whether or not a debit card was
used, we can use the binomial...

Let X be normally distributed with mean 3 and variance
σ2 . Let Y = 3X + 7.
A) Find the mean, variance, and PDF of Y. (The other listed
solution does not have the PDF.)
B) Assuming P(Y ≤ 17) = .6331, find σ2 .
C) Assuming σ2 = 1, find the PDF of W =
(|Y|)1/2 + 1.

QUESTION 4
The number of laptops sold per day by Karisma Technology Berhad
is given by the following probability distribution function.
Number of laptops (x)
0
1
2
3
4
P(X=x)
0.2
0.3
a
a
b
If the mean of sales per day is 1.7, find
the values of a and b.

3. Let X be a continuous random variable with PDF
fX(x) = c / x^1/2, 0 < x < 1.
(a) Find the value of c such that fX(x) is indeed a PDF. Is this
PDF bounded?
(b) Determine and sketch the graph of the CDF of X.
(c) Compute each of the following:
(i) P(X > 0.5).
(ii) P(X = 0).
(ii) The median of X.
(ii) The mean of X.

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