8. In a supermarket, the weight of apples has an approximately normal distribution with the mean of 190 gram and the standard deviation of 12 gram; the weight of the pears also has an approximately normal distribution with the mean of 210 gram and the standard deviation of 15 gram. (a) When an apple and a pear are randomly selected, what is the probability that the apple weights more than the pear? (b) If Tom randomly buys 30 apples and 20 pears, what is the probability that their total weight exceeds 10kg (10kg = 10, 000g)?
8. In a supermarket, the weight of apples has an approximately normal distribution with the mean of 190 gram and the standard deviation of 12 gram; the weight of the pears also has an approximately normal distribution with the mean of 210 gram and the standard deviation of 15 gram. (a) When an apple and a pear are randomly selected, what is the probability that the apple weights more than the pear? (b) If Tom randomly buys 30 apples and 20 pears, what is the probability that their total weight exceeds 10kg (10kg = 10, 000g)?
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 #8
![1. (a)
When five dice are rolled, what is the probability that at least 4 "ones" come up?
(b)
1
When five dice are rolled, what is the probability of getting a full-house?
(ex: aaabb)
2. In a box, there are 3 fair coins, 2 special coins with heads on both sides and 5 special coins
with tails on both sides. A coin is randomly selected and flipped.
(a)
] If a head comes up, what is the probability that the selected coin is a special
coin with heads on both sides?
(b) [
3. Consider a standard deck of 52 cards. Five cards are randomly drawn by each of three
players.
(a)r
(b)
When the same coin is flipped again, if a head still comes up, what is the
probability that the selected coin is a special coin with heads on both sides?
4. In an office, assume the number of arriving telephone calls has a Poisson distribution with an
average rate of 10 calls per hour.
(a) [
(b) [
(a)
(b)
What is the probability that at least one player receives at least one spade?
What is the probability that at least one player receives 5 spades?
5. In a country, citizens' annual incomes are normally distributed with a mean of $20,000 and a
standard deviation of $4,000.
(a)
(b)
What is the probability that exactly 5 calls arrive in a given 40 minutes?
Assume the office opens at 9:00AM. What is the probability that the first call
arrives between 9:05AM and 9:15AM?
(a)
(b)
] When a citizen is randomly surveyed, what is the probability that his annual
income is below $17,000?
6. Let X be the continuous random variable with the probability density function
f(x) = {(2x+5)/44 if1 ≤x≤5
otherwise
] When 10 citizens are randomly surveyed, what is the probability that their
average annual incomes are below $17,000?
7. When two dice are tossed, let the random variable X represent the minimum value of the two
dice and let the random variable Y represent the absolute value of the difference of the two
dice.
Find E(X) and Var (X).
]Find the cumulative distribution function of X.
Find the joint probability function.
] Find the marginal probability density function of X and Y, and determine
whether X and Y are independent random variables.
15 gram.
(a)
8. In a supermarket, the weight of apples has an approximately normal distribution with the
mean of 190 gram and the standard deviation of 12 gram; the weight of the pears also has an
approximately normal distribution with the mean of 210 gram and the standard deviation of
When an apple and a pear are randomly selected, what is the probability that
the apple weights more than the pear?
(b) L
If Tom randomly buys 30 apples and 20 pears, what is the probability that their
total weight exceeds 10kg (10kg = 10, 000g)?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F33eba9e5-eb7d-44a1-93e3-ed0ee897e17f%2F1e3259ae-82d5-46a7-8a06-ffcb9a46486d%2Faqlxv2l_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. (a)
When five dice are rolled, what is the probability that at least 4 "ones" come up?
(b)
1
When five dice are rolled, what is the probability of getting a full-house?
(ex: aaabb)
2. In a box, there are 3 fair coins, 2 special coins with heads on both sides and 5 special coins
with tails on both sides. A coin is randomly selected and flipped.
(a)
] If a head comes up, what is the probability that the selected coin is a special
coin with heads on both sides?
(b) [
3. Consider a standard deck of 52 cards. Five cards are randomly drawn by each of three
players.
(a)r
(b)
When the same coin is flipped again, if a head still comes up, what is the
probability that the selected coin is a special coin with heads on both sides?
4. In an office, assume the number of arriving telephone calls has a Poisson distribution with an
average rate of 10 calls per hour.
(a) [
(b) [
(a)
(b)
What is the probability that at least one player receives at least one spade?
What is the probability that at least one player receives 5 spades?
5. In a country, citizens' annual incomes are normally distributed with a mean of $20,000 and a
standard deviation of $4,000.
(a)
(b)
What is the probability that exactly 5 calls arrive in a given 40 minutes?
Assume the office opens at 9:00AM. What is the probability that the first call
arrives between 9:05AM and 9:15AM?
(a)
(b)
] When a citizen is randomly surveyed, what is the probability that his annual
income is below $17,000?
6. Let X be the continuous random variable with the probability density function
f(x) = {(2x+5)/44 if1 ≤x≤5
otherwise
] When 10 citizens are randomly surveyed, what is the probability that their
average annual incomes are below $17,000?
7. When two dice are tossed, let the random variable X represent the minimum value of the two
dice and let the random variable Y represent the absolute value of the difference of the two
dice.
Find E(X) and Var (X).
]Find the cumulative distribution function of X.
Find the joint probability function.
] Find the marginal probability density function of X and Y, and determine
whether X and Y are independent random variables.
15 gram.
(a)
8. In a supermarket, the weight of apples has an approximately normal distribution with the
mean of 190 gram and the standard deviation of 12 gram; the weight of the pears also has an
approximately normal distribution with the mean of 210 gram and the standard deviation of
When an apple and a pear are randomly selected, what is the probability that
the apple weights more than the pear?
(b) L
If Tom randomly buys 30 apples and 20 pears, what is the probability that their
total weight exceeds 10kg (10kg = 10, 000g)?
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