Susan commutes daily from her home to her office. The average time for a one-way trip is 24 minutes with a standard deviation of 3.8 minutes. Assume that the trip time follows a normal distribution. a) If she leaves her house at 8:30 am and coffee is served at the office from 8:50 am until 9:00 am, what is the probability that coffee is not served at the time she gets her office? b) Find the length of time below which we find the fastest 15% of the trips. c) A trip to a client's office from her home takes 30 more minutes than twice the time to her own office. Let W be the time for a trip to the client's office. (i) Find mean, variance and moment generating function of W. Identify the distribution of W. (ii) Find the probability that a trip to the client's office takes more than 1 hour but less than 1.5 hour.
Susan commutes daily from her home to her office. The average time for a one-way trip is 24 minutes with a standard deviation of 3.8 minutes. Assume that the trip time follows a normal distribution. a) If she leaves her house at 8:30 am and coffee is served at the office from 8:50 am until 9:00 am, what is the probability that coffee is not served at the time she gets her office? b) Find the length of time below which we find the fastest 15% of the trips. c) A trip to a client's office from her home takes 30 more minutes than twice the time to her own office. Let W be the time for a trip to the client's office. (i) Find mean, variance and moment generating function of W. Identify the distribution of W. (ii) Find the probability that a trip to the client's office takes more than 1 hour but less than 1.5 hour.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.5: Comparing Sets Of Data
Problem 26PFA
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Step 1: Summarise the provided information
VIEWStep 2: Find the probability that coffee is not served when she gets to office
VIEWStep 3: Find the time below which fastest 15% of the trips were made
VIEWStep 4: Find mean, variance, MGF and distribution of W
VIEWStep 5: Compute the probability P(60<W<90)
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