Answered: Assume that thermometer readings are…

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.3: Measures Of Spread

Problem 3CYU

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Question

Assume that thermometer readings are normally distributed with a mean of

0°C

and a standard deviation of

1.00°C.

A thermometer is randomly selected and tested. For the casebelow, draw a sketch, and find the probability of the reading. (The given values are in Celsius degrees.)

Between

0.25

and 1.25

Click to view page 1 of the table.

Click to view page 2 of the table.

Draw a sketch. Choose the correct graph below.

z=0.25z=1.25

A graph with a bell-shaped curve, divided into 3 regions by 2 lines from top to bottom, both on the right side. The region between the 2 lines is shaded. Moving from left to right, the z-axis below the first line is labeled "z=0.25". The z-axis below the second line is labeled "z=1.25".

z=0.25z=1.25

A graph with a bell-shaped curve, divided into 3 regions by 2 lines from top to bottom, both on the right side. Moving from left to right, the region left of the first line is shaded. The z-axis below this line is labeled "z=0.25". The z-axis below the second line is labeled "z=1.25".

z=0.25z=1.25

A graph with a bell-shaped curve, divided into 3 regions by 2 lines from top to bottom, both on the right side. Moving from left to right, the region right of the second line is shaded. The z-axis below this line is labeled "z=1.25". The z-axis below the first line is labeled "z=0.25".

The probability of getting a reading between

0.25°C

and

1.25°C

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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