Answered: Fawns between 1 and 5 months old have a…

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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Question

Fawns between 1 and 5 months old have a body weight that is approximately normally distributed with mean ? = 28.4 kilograms and standard deviation ? = 4.1 kilograms. Let x be the weight of a fawn in kilograms.

Convert the following x intervals to z intervals. (Round your answers to two decimal places.)

x < 30
z < ____

19 < x
___ < z

32 < x < 35
____ < z < ____

Convert the following z intervals to x intervals. (Round your answers to one decimal place.)

−2.17 < z
___ < x

z < 1.28
x < ____

−1.99 < z < 1.44
____< x < ____

If a fawn weighs 14 kilograms, would you say it is an unusually small animal? Explain using z values and the figure above.

Yes. This weight is 3.51 standard deviations below the mean; 14 kg is an unusually low weight for a fawn.

Yes. This weight is 1.76 standard deviations below the mean; 14 kg is an unusually low weight for a fawn.

No. This weight is 3.51 standard deviations below the mean; 14 kg is a normal weight for a fawn.

No. This weight is 3.51 standard deviations above the mean; 14 kg is an unusually high weight for a fawn.

No. This weight is 1.76 standard deviations above the mean; 14 kg is an unusually high weight for a fawn.

If a fawn is unusually large, would you say that the z value for the weight of the fawn will be close to 0, −2, or 3? Explain.

It would have a negative z, such as −2.

It would have a large positive z, such as 3.

It would have a z of 0.

The Standard Normal Distribution
(u = 0, o = 1)
%3D
3
-2
3
68% of area
95% of area
99.7% of area

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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