5.5-9 a only (b) For the of n in part P(Yand the of the of a prepackaged(a) If X and Y have the sameX>0.2).5.55.5-7. Suppose that the distribution of the weight of aprepackaged "l-pound bag" of carrots is N(1.18, 0.07-)ou(3)-pound bag" of carrots is N(3.22, 0.09). Selectingbags at random, find the probability that the sum of three1-pound bags exceeds the weight of one 3-pound bag.HINT: First determine the distribution of Y, the sum of thethree, and then compute P(Y > W), where W is the weightof the 3-pound bag.5.5-8. Let X denote the wing length in millimeters of amale gallinule and Y the wing length in millimeters of afemale gallinule. Assume that X is N(184.09, 39.37) andY is N(171.93, 50.88) and that X and Y are independent.If a male and a female gallinule are captured, what is theprobability that X is greater than Y?5.5-9. Suppose that the length of life in hours (say, X) ofa light bulb manufactured by company A is N(800, 14400)and the length of life in hours (say, Y) of a light bulbmanufactured by company B is N(850, 2500). One bulb israndomly selected from each company and is burned until"death."(a) Find the probability that the length of life of the bulbfrom company A exceeds the length of life of the bulbfrom 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 hasa lifetime that has a mean of 800 hours, a standard devia-tion of 100 hours, and a normal distribution. A light bulbis replaced by another as soon as it burns out. Assuming

Name: 5.5-9 a only (b) For the of n in part P(Yand the of the of a prepackag
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Description: 5.5-9 a only (b) For the of n in part P(Yand the of the of a prepackaged(a) If X and Y have the sameX>0.2).5.55.5-7. Suppose that the distribution of the weight of aprepackaged "l-pound bag" of carrots is N(1.18, 0.07-)ou(3)-pound bag" of carrots is

5.5-9 (a) The random variable X has the distribution N(800, 14,400) and the random variable Y has the distribution N(850, 2,500). It is known that if X~NμX , σX2 and Y~NμY , σY2, then X-Y~NμX-μY , σX2+σY2. The distribution of variable X-Y is given by, μX-μY =800-850=-50 σX2+σY2=14,400+2,500=16,900 The distribution of variable X-Y is N(-50, 16,900). The standard deviation for X-Y is, σX-Y=σX-Y2=16,900=130The z-score for X-Y being at least 15 is, z=x-μσ=15--50130=65130=0.50 The probability of z less than 0.50 can be obtained using the excel formula “=NORM.S.DIST(0.50,TRUE)”. The probability value is 0.6915. The probability is, PX-Y≥15=Pz≥0.50=1-Pz<0.50=1-0.6915=0.3085 Thus, the 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 is 0.3085.

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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." 14 (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 leanct

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." 14 (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 leanct

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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Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.

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Question

5.5-9 a only

(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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