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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)?

College Algebra
College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 6ECP: In Pennsylvania’s Cash 5 game, a player chooses five different numbers from 1 to 43. If these five...
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Need help with this probability question please 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)?
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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