Introductory Statistics (10th Edition)
10th Edition
ISBN: 9780321989178
Author: Neil A. Weiss
Publisher: PEARSON
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Chapter 6.1, Problem 40E
a.
To determine
Sketch the distribution of the variable x.
b.
To determine
Obtain the standardized version z of x.
c.
To determine
Sketch the distribution of z.
d.
To determine
Fill in the given blank.
e.
To determine
Fill in the given blank.
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Green Sea Urchins. From the paper “Effects of Chronic Nitrate Exposure on Gonad Growth in Green Sea Urchin Strongylocentrotus droebachiensis” (Aquaculture,Vol. 242, No. 1–4, pp. 357–363) by S. Siikavuopio et al., we found that weights of adult green sea urchins are normally distributed with mean 52.0 g and standard deviation 17.2 g. Let x denote weight of adult green sea urchins.
a. Sketch the distribution of the variable x.
b. Obtain the standardized version, z, of x.
c. Identify and sketch the distribution of z.
d. The percentage of adult green sea urchins with weights between 50 g and 60 g is equal to the area under the standard normal curve between _______ and _______.
e. The percentage of adult green sea urchins with weights above 40 g is equal to the area under the standard normal curve that lies to the _______of _______.
An article in Environment International ["influence of Water Temperature and Shower
Head Office Size on the release Radon During Showering" (1992, Vol. 18(4)] described an
experiment in which the amount of radon released in showers was imvestigated. Radon-enriched
water was used in the experiment, and six different orifice diameters were tested in shower
heads. The data from the experiment are shown in the following table.
5.
Orifice Diameter
0.37
0.51
0.71
1.02
Radon Released ()
83
75
73
72
83
85
79
79
74
76
77
67
74
74
1.40
62
62
67
69
1.99
60
64
66
(a) Does the size of the orifice affect the mean percentage of radon released? Use a=0.05.
(b) Find a 95% confidence interval on the mean percent of radon released when the orifice
diameter is 1.40.
The article “Ozone for Removal of Acute Toxicity from Logyard Run-off” (M. Zenaitis and S. Duff, Ozone Science and Engineering, 2002: 83–90) presents chemical analyses of runoff water from sawmills in British Columbia. Included were measurements of pH for six water specimens: 5.9, 5.0, 6.5, 5.6, 5.9, 6.5. Assume that these are a random sample of water specimens from a normal population. a) Find a 98% prediction interval for a pH of a single specimen. b) Find a tolerance interval for the pH that includes 95% of the specimens with 95% confidence.
Chapter 6 Solutions
Introductory Statistics (10th Edition)
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