**Probability Distribution of Customer Service Telephone Lines**A business has six customer service telephone lines. Let $ x $ denote the number of lines in use at any given time. Suppose that the probability distribution of $ x $ is as follows:| x | 0 | 1 | 2 | 3 | 4 | 5 | 6 ||----|-----|-----|-----|-----|-----|-----|-----|| p(x) | 0.05 | 0.10 | 0.18 | 0.39 | 0.18 | 0.08 | 0.02 |**Events and Probability Calculations**Write each of the following events in terms of $ x $, and then calculate the probability of each one.(a) **At most three lines are in use**: Event: $ x \leq 3 $ \[ P(x \leq 3) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3) \] \[ = 0.05 + 0.10 + 0.18 + 0.39 = 0.72 \](b) **Fewer than three lines are in use**: Event: $ x < 3 $ \[ P(x < 3) = P(x = 0) + P(x = 1) + P(x = 2) \] \[ = 0.05 + 0.10 + 0.18 = 0.33 \](c) **At least three lines are in use**: Event: $ x \geq 3 $ \[ P(x \geq 3) = P(x = 3) + P(x = 4) + P(x = 5) + P(x = 6) \] \[ = 0.39 + 0.18 + 0.08 + 0.02 = 0.67 \](d) **Between two and five lines (inclusive) are in use**: Event: $ 2 \leq x \leq 5 $ \[ P(2 \leq x \

As per our guidelines we are suppose to answer only three sub parts. Required probability is P(X≤3)

Answered: A Business has six customer service…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The chance of an IRS audit for a tax return with over $25,000 in income is about 2% per year. We are interested in the expected number of audits a person with that income has in a 16-year period. Assume each year is independent. Part (a) Part (b) List the values that X may take on. X=0, 1, 2,..., 15, 16 OX= 1, 2, 3, OX= 1, 2, 3, OX=1,2,3,... 15, 16 98, 99, 100 Part (c) Give the distribution of X X-B 0.02 □ Part (d) How many audits are expected in a 16-year period? (Round your answer to two decimal places.) 0.32 audits Part (e) Find the probability that a person is not audited at all. (Round your answer to four decimal places.) Part (1) Find the probability that a person is audited more than twice. (Round your answer to four decimal places.)
Let X = {Email, In Person, Instant Message, Text Message}; P(Email) = 0.06 P(In Person) = 0.55 P(Instant Message) = 0.24 P(Text Message) = 0.15 Is this model a probability distribution? A. Yes. B. No. C. Maybe.
A deck of four (4) cards has exactly one (1) color printed on each face – blue, yellow, red, or green. You have two (2) identical decks of this type. In this game, you randomly select a card from each of the two decks. Your score is the number of blue cards drawn – refer to this quantity as X. The probability distribution is below: X P(X) 0 0.5625 1 0.375 2 0.0625 What is the average number of blue cards drawn? What is the probability that at most one blue card is drawn?
High school students in Michigan sometimes get "snow days" in the winter when the roads are so bad that school is canceled for the day. Define the random variableX = the number of snow days at a certain high school in Michigan for a randomly selected school year. Suppose the table below gives the probability distribution of X. 1. Value x, 1. 3 4 5 6 7 8 9 10 Probability p, ? 0.19 0.14 0.10 0.07 0.05 0.04 0.04 0.02 0.01 0.01 (a) Write the event “the school year has O snow days" in terms of X. Then find its probability. (b) At this high school, if more than 5 snow days are used over the course of the year, students are required to make up the time at the end of the school year. What's the probability that a randomly selected school year will require make-up days?
The following table lists certain values of x and their probabilities. Verify whether or not it represents a valid probability distribution. P(x) 0 0.31 1 0.30 2 0.19 3 0.16 The table a valid probability distribution.
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Assume that 12 jurors are randomly selected from a population in which 60% of the people are Mexican-Americans. Refer to the probability distribution table below and find the indicated probabilities. Number of Mexican-Americans Probability 0 0 1 0.0003 2 0.0025 3 0.0125 4 0.042 5 0.1009 6 0.1766 7 0.227 8 0.2128 9 0.1419 10 0.0639 11 0.0174 12 0.0022 a) Find the probability of at most 4 Mexican-Americans among 12 jurors. Give answer as a decimal. b) Find the probability of more than 4 Mexican-Americans among 12 jurors. Give answer as a decimal.
Do you carpool? Let X represent the number of occupants in a randomly chosen car on a certain stretch of highway during morning commute hours. A survey of cars showed that the probability distribution of X is as follows. x 1 2 3 4 5 Px 0.68 0.14 0.08 0.02 0.08 Send data to Excel Part 1 of 7 (a) Find P1 . P1 = .68 Part 2 of 7 (b) Find P (greater than or equal to 2 ). P (greater than or equal to 2 ) = .32 Part 3 of 7 (c) Find the probability that a car has only one occupant. The probability that a car has only one occupant is . Part 4 of 7 (d) Find the probability that a car has fewer than four occupants. The probability that a car has fewer than four occupants is . Part 5 of 7 (e) Compute the mean μx .…
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A deck of four (4) cards has exactly one (1) color printed on each face – blue, yellow, red, or green. You have two (2) identical decks of this type. In this game, you randomly select a card from each of the two decks. Your score is the number of blue cards drawn – refer to this quantity as X. The probability distribution is below: X P(X) 0 0.5625 1 0.375 2 0.0625 1. If we replaced the yellow card in the first deck with another blue card, what would be the probability of drawing two blue cards? 2. If we replaced the yellow card in the first deck with another blue card, what distribution would the variable X follow?
A probability distribution function has which characteristic(s)? (Select all characteristic that applies.) Each probability is between zero and one, inclusive. Each probability is larger than one. The sum of the probabilities is one. The sum of the probabilities is larger than one.

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