Answered: 50 40 30 20 10 0.005 0.010 0.015 0.020…

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.3: Measures Of Spread

Problem 18HP

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Question

Soup A machine is supposed to fill cans with 16 oz
of soup. Of course there, will be some variation in the
amount actually dispensed, and measurement errors are
often approximately normally distributed. The manager
would like to understand the variability of the variances of
the samples, so he collects information from the last 250
batches of size 10 and plots a histogram of the variances:a) Would a Normal model be a useful model for this
sampling distribution? Explain.
b) The mean of this distribution is 0.009 and the SD is
0.004. Would you expect about 95% of the samples
to have their variances within 0.008 of 0.009? Why or
why not?

50
40
30
20
10
0.005
0.010
0.015
0.020
Sample Variance
Frequency

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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