Answered: Hoop Fever is an arcade basketball game…

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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PROBLEM:

Hoop Fever is an arcade basketball game in which a player has 60 seconds to make a baskets as possible. Morgan and Tim play head-to-head every Tuesday. Let M = the number of baskets made by Morgan and T = the number of baskets made by Tim in a randomly selected match. Based on previous matches, we know that uM = 39.8 and ur = 31.2. Let D= M-T. Calculate and interpret the mean of D.

PROBLEM:

In Hoop Fever, a player has 60 seconds to make as many baskets as possible. Morgan and Tim play head-to-head every Tuesday. Let M = the number of baskets made by Morgan and T= the number of baskets made by Tim in a randomly selected match. Based on previous matches, we know that ow = 5.7 and or = 10.3. Assume that these two random variables are independent. Define D= M - T. Earlier, we found that up = 8.6. Calculate and interpret the standard deviation of D.

PROBLEM:

A match of Hoop Fever gives each player 60 seconds to make as many baskets as possible. Morgan and Tim play head-to-head every Tuesday. Suppose that M = the number of baskets made by Morgan in a randomly selected match follows an approximately Normal distribution with uM = 39.8 and uM = 5.7. Suppose that T= the number of baskets made by Tim in a randomly selected match follows an approximately Normal distribution with Um= 31.2 and Ot= 10.3. Assume that these two random variables are independent and define D= M-T.

(a) Describe the distribution of D.

(b) What is the probability that Morgan will make more baskets than Tim in a randomly selected match?

of X and
ALTERNATE EXAMPLE (page 389)
Hoop Fever
Mean of a sum or difference of random variables
PROBLEM:
Hoop Fever is an arcade basketball game in which a player has 60 seconds to make as many
baskets as possible. Morgan and Tim play head-to-head every Tuesday. Let M = the number
of baskets made by Morgan and T = the number of baskets made by Tim in a randomly
selected match. Based on previous matches, we know that µM = 39.8 and ur = 31.2. Let
D = M – T. Calculate and interpret the mean of D.
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%D
ALTERNATE EXAMPLE (page 392)
More Hoop Fever
SD of a sum or difference of random variables
PROBLEM:
In Hoop Fever, a player has 60 seconds to make as many baskets as possible. Morgan and
Tim play head-to-head every Tuesday. Let M = the number of baskets made by Morgan and
T = the number of baskets made by Tim in a randomly selected match. Based on previous
matches, we know that oM = 5.7 and oT = 10.3. Assume that these two random variables are
independent. Define D = M – T. Earlier, we found that uD = 8.6. Calculate and interpret the
standard deviation of D.
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%3D
%3D
%3D

ALTERNATE EXAMPLE (page 395)
rot
Who will win?
Combining Normal random variables
PROBLEM:
A match of Hoop Fever gives each player 60 seconds to make as many baskets as possible.
Morgan and Tim play head-to-head every Tuesday. Suppose that M = the number of baskets
made by Morgan in a randomly selected match follows an approximately Normal
distribution with uM = 39.8 and uM = 5.7. Suppose that T = the number of baskets made by
Tim in a randomly selected match follows an approximately Normal distribution with
31.2 and o, = 10.3. Assume that these two random variables are independent and
%3D
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define D = M -T.
(a) Describe the distribution of D.
(b) What is the probability that Morgan will make more baskets than Tim in a randomly
selected match?

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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