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1. The waiting time at a bus stop is uniformly distributed between 1 and 12 minute. a. What is the probability density function? b. What is the probability that the rider waits 8 minutes or less? c. What is the expected waiting time? d. What is standard deviation of waiting time?

1. The waiting time at a bus stop is uniformly distributed between 1 and 12 minute. a. What is the probability density function? b. What is the probability that the rider waits 8 minutes or less? c. What is the expected waiting time? d. What is standard deviation of waiting time?

A First Course in Probability (10th Edition)
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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1. The waiting time at a bus stop is unifomly distributed between 1 and 12 minute. a. What is the probability density function? b. What is the probability that the rider waits 8 minutes or less? c. What is the expected waiting time? d. What is standard deviation of waiting time? 2. Assume the weight of a randomly chosen American passenger car is a uniformly distributed random variable ranging from 2,500 pounds to 4,500 pounds. a. What is the mean and standard deviation of weight of a randomly chosen vehicle? b. What is the probability that a vehicle will weigh less than 3,000 pounds? c. More than 3,900 pounds? d. Between 3,000 and 3,800 pounds? 3. The blood pressure of adult males is normally distributed with a mean of 125mm/hg and a standard deviation of 8. a. What % of men have blood pressure of 129mm/Hg or more? b. What % of men have blood pressure of 131-4mm/Hg or more? c. What % of men have blood pressure of 126-6mm/Hg or more? d. What % of men have blood pressure of 126-6mm/Hg or less? 4. The salaries of UConn professors is approximately nomally distrībuted. Suppose you know that 33 percent of professors earn less than $80,000. Also 33 percent eam more than $120,000. (a) What is the probability that a UConn professor makes more than $100,000? (b) What is the probability that a UConn professor makes between $70,000 and $80,000? 5. A coin is tossed 400 times, use the normal approximation to binomial to find the probability of obtaining (a) between 185 and 210 heads inclusive (b) exactly 205 heads (c) less than 176 or more than 227 heads
Transcribed Image Text:1. The waiting time at a bus stop is unifomly distributed between 1 and 12 minute. a. What is the probability density function? b. What is the probability that the rider waits 8 minutes or less? c. What is the expected waiting time? d. What is standard deviation of waiting time? 2. Assume the weight of a randomly chosen American passenger car is a uniformly distributed random variable ranging from 2,500 pounds to 4,500 pounds. a. What is the mean and standard deviation of weight of a randomly chosen vehicle? b. What is the probability that a vehicle will weigh less than 3,000 pounds? c. More than 3,900 pounds? d. Between 3,000 and 3,800 pounds? 3. The blood pressure of adult males is normally distributed with a mean of 125mm/hg and a standard deviation of 8. a. What % of men have blood pressure of 129mm/Hg or more? b. What % of men have blood pressure of 131-4mm/Hg or more? c. What % of men have blood pressure of 126-6mm/Hg or more? d. What % of men have blood pressure of 126-6mm/Hg or less? 4. The salaries of UConn professors is approximately nomally distrībuted. Suppose you know that 33 percent of professors earn less than $80,000. Also 33 percent eam more than $120,000. (a) What is the probability that a UConn professor makes more than $100,000? (b) What is the probability that a UConn professor makes between $70,000 and $80,000? 5. A coin is tossed 400 times, use the normal approximation to binomial to find the probability of obtaining (a) between 185 and 210 heads inclusive (b) exactly 205 heads (c) less than 176 or more than 227 heads
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