1. You are to model the daytime temperature of the Mojave desert during the summer time.Temperatures in the desert are modeled to follow a normal distribution with μ = 102 Fahrenheitand variance σ2 = 25 Fahrenheit. d. Say X is the random variable that denotes the temperature during the desert day. Whatdistribution does 0.55 X-17.6 follow? State the type of distribution, and all parameters.e. Now say you relax the normality assumption from the model, and you observe 25 days temper-atures (X₁, X2, X25) from some unknown distribution. What is the approximate distributionEX? State the approximate type ofnof the sample mean of these daily temperatures, Xi=1distribution and all parameters....=-nf. Continuing with part e, you now transform each temperature from Fahrenheit to Celsius. Theconversion isCelsius 0.55*Fahrenheit-17.6. What approximate distribution does the sample mean in Celsiusfollow? State the type and parameters.

Let X be the temperature during the desert day. From the given information, X follows normal…

You are to model the daytime temperature of the Mojave desert during the summer time. Temperatures in the desert are modeled to follow a normal distribution with μ = 102 Fahrenheit and variance σ2 = 25 Fahrenheit.

You are to model the daytime temperature of the Mojave desert during the summer time. Temperatures in the desert are modeled to follow a normal distribution with μ = 102 Fahrenheit and variance σ2 = 25 Fahrenheit.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 22PFA

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Question

1. You are to model the daytime temperature of the Mojave desert during the summer time.
Temperatures in the desert are modeled to follow a normal distribution with μ = 102 Fahrenheit
and variance σ2 = 25 Fahrenheit.

d. Say X is the random variable that denotes the temperature during the desert day. What
distribution does 0.55 X-17.6 follow? State the type of distribution, and all parameters.
e. Now say you relax the normality assumption from the model, and you observe 25 days temper-
atures (X₁, X2, X25) from some unknown distribution. What is the approximate distribution
EX? State the approximate type of
n
of the sample mean of these daily temperatures, X
i=1
distribution and all parameters.
...
=
-
n
f. Continuing with part e, you now transform each temperature from Fahrenheit to Celsius. The
conversion is
Celsius 0.55*Fahrenheit-17.6. What approximate distribution does the sample mean in Celsius
follow? State the type and parameters.

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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