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.
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...
Related questions
Question
Transcribed Image Text: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.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
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)
VIEWSolution
VIEW
Trending now
This is a popular solution!
Step by step
Solved in 6 steps with 10 images
Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON