5.5-7
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Question
5.5-7
![(b) For the of n in part P(Y
and the of the of a prepackaged
(a) If X and Y have the same
X>0.2).
5.5
5.5-7. Suppose that the distribution of the weight of a
prepackaged "l-pound bag" of carrots is N(1.18, 0.07-)
ou
(3)
-pound bag" of carrots is N(3.22, 0.09). Selecting
bags at random, find the probability that the sum of three
1-pound bags exceeds the weight of one 3-pound bag.
HINT: First determine the distribution of Y, the sum of the
three, and then compute P(Y > W), where W is the weight
of the 3-pound bag.
5.5-8. Let X denote the wing length in millimeters of a
male gallinule and Y the wing length in millimeters of a
female gallinule. Assume that X is N(184.09, 39.37) and
Y is N(171.93, 50.88) and that X and Y are independent.
If a male and a female gallinule are captured, what is the
probability that X is greater than Y?
5.5-9. Suppose that the length of life in hours (say, X) of
a light bulb manufactured by company A is N(800, 14400)
and the length of life in hours (say, Y) of a light bulb
manufactured by company B is N(850, 2500). One bulb is
randomly selected from each company and is burned until
"death."
(a) Find the probability that the length of life of the bulb
from company A exceeds the length of life of the bulb
from company B by at least 15 hours.
(b) Find the probability that at least one of the bulbs
"lives" for at least 920 hours.
5.5-10. A consumer buys n light bulbs, each of which has
a lifetime that has a mean of 800 hours, a standard devia-
tion of 100 hours, and a normal distribution. A light bulb
is replaced by another as soon as it burns out. Assuming](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F26fe8f9d-a829-4ffe-94fa-74d9058056a0%2F619f478e-2de5-451a-bf61-449202facea6%2Ff07eex_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(b) For the of n in part P(Y
and the of the of a prepackaged
(a) If X and Y have the same
X>0.2).
5.5
5.5-7. Suppose that the distribution of the weight of a
prepackaged "l-pound bag" of carrots is N(1.18, 0.07-)
ou
(3)
-pound bag" of carrots is N(3.22, 0.09). Selecting
bags at random, find the probability that the sum of three
1-pound bags exceeds the weight of one 3-pound bag.
HINT: First determine the distribution of Y, the sum of the
three, and then compute P(Y > W), where W is the weight
of the 3-pound bag.
5.5-8. Let X denote the wing length in millimeters of a
male gallinule and Y the wing length in millimeters of a
female gallinule. Assume that X is N(184.09, 39.37) and
Y is N(171.93, 50.88) and that X and Y are independent.
If a male and a female gallinule are captured, what is the
probability that X is greater than Y?
5.5-9. Suppose that the length of life in hours (say, X) of
a light bulb manufactured by company A is N(800, 14400)
and the length of life in hours (say, Y) of a light bulb
manufactured by company B is N(850, 2500). One bulb is
randomly selected from each company and is burned until
"death."
(a) Find the probability that the length of life of the bulb
from company A exceeds the length of life of the bulb
from company B by at least 15 hours.
(b) Find the probability that at least one of the bulbs
"lives" for at least 920 hours.
5.5-10. A consumer buys n light bulbs, each of which has
a lifetime that has a mean of 800 hours, a standard devia-
tion of 100 hours, and a normal distribution. A light bulb
is replaced by another as soon as it burns out. Assuming
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