Calculus For The Life Sciences
2nd Edition
ISBN: 9780321964038
Author: GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher: Pearson Addison Wesley,
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Chapter 13.CR, Problem 63CR
Yeast cells The famous statistician William Gosset, who worked for Guinness brewery in Ireland, took measurements of the number of yeast cells per square in a hemocytometer.Source: Statistical Methods in Biology. The data can be closely described by a Poisson distribution with
a. Fewer than 3 yeast cells
b. Exactly 3 yeast cells
c. At least 3 yeast cells
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Question 1:
If a barometer were built using oil (p = 0.92 g/cm³) instead of mercury (p =
13.6 g/cm³), would the column of oil be higher than, lower than, or the same as the
column of mercury at 1.00 atm? If the level is different, by what factor? Explain. (5 pts)
Solution:
A barometer works based on the principle that the pressure exerted by the liquid column
balances atmospheric pressure. The pressure is given by:
P = pgh
Since the atmospheric pressure remains constant (P = 1.00 atm), the height of the
liquid column is inversely proportional to its density:
Step 1: Given Data
PHg
hol=hgx
Poil
• Density of mercury: PHg = 13.6 g/cm³
Density of oil: Poil = 0.92 g/cm³
• Standard height of mercury at 1.00 atm: hμg
Step 2: Compute Height of Oil
= 760 mm = 0.760 m
13.6
hoil
= 0.760 x
0.92
hoil
= 0.760 × 14.78
hoil
= 11.23 m
Step 3: Compare Heights
Since oil is less dense than mercury, the column of oil must be much taller than that of
mercury. The factor by which it is taller is:
Final…
Chapter 13 Solutions
Calculus For The Life Sciences
Ch. 13.1 - Repeat Example 1a for the function f(x)=2x2 on...Ch. 13.1 - Prob. 2YTCh. 13.1 - Prob. 3YTCh. 13.1 - Prob. 1ECh. 13.1 - Prob. 2ECh. 13.1 - Prob. 3ECh. 13.1 - Prob. 4ECh. 13.1 - Prob. 5ECh. 13.1 - Prob. 6ECh. 13.1 - Prob. 7E
Ch. 13.1 - Prob. 8ECh. 13.1 - Prob. 9ECh. 13.1 - Prob. 10ECh. 13.1 - Prob. 11ECh. 13.1 - Prob. 12ECh. 13.1 - Prob. 13ECh. 13.1 - Prob. 14ECh. 13.1 - Prob. 15ECh. 13.1 - Prob. 16ECh. 13.1 - Prob. 17ECh. 13.1 - Prob. 18ECh. 13.1 - Prob. 19ECh. 13.1 - Prob. 20ECh. 13.1 - Prob. 21ECh. 13.1 - Prob. 22ECh. 13.1 - Find the cumulative distribution function for the...Ch. 13.1 - Prob. 24ECh. 13.1 - Prob. 25ECh. 13.1 - Prob. 26ECh. 13.1 - Prob. 27ECh. 13.1 - Prob. 28ECh. 13.1 - Show that each function defined as follows is a...Ch. 13.1 - Prob. 30ECh. 13.1 - Show that each function defined as follows is a...Ch. 13.1 - Prob. 32ECh. 13.1 - Prob. 33ECh. 13.1 - Prob. 34ECh. 13.1 - Prob. 35ECh. 13.1 - Prob. 36ECh. 13.1 - Prob. 45ECh. 13.1 - Prob. 47ECh. 13.1 - Prob. 48ECh. 13.1 - Prob. 49ECh. 13.2 - YOUR TURN 1 Repeat Example 1 for the probability...Ch. 13.2 - Prob. 2YTCh. 13.2 - Prob. 3YTCh. 13.2 - In Exercises 1-8, a probability density function...Ch. 13.2 - Prob. 2ECh. 13.2 - Prob. 3ECh. 13.2 - Prob. 4ECh. 13.2 - Prob. 5ECh. 13.2 - Prob. 6ECh. 13.2 - Prob. 7ECh. 13.2 - Prob. 8ECh. 13.2 - Prob. 9ECh. 13.2 - Prob. 10ECh. 13.2 - Prob. 11ECh. 13.2 - Prob. 12ECh. 13.2 - Prob. 13ECh. 13.2 - Prob. 14ECh. 13.2 - Prob. 15ECh. 13.2 - Prob. 16ECh. 13.2 - Prob. 17ECh. 13.2 - Prob. 18ECh. 13.2 - Prob. 19ECh. 13.2 - Prob. 20ECh. 13.2 - Prob. 21ECh. 13.2 - Prob. 22ECh. 13.2 - Prob. 23ECh. 13.2 - Prob. 24ECh. 13.2 - Length of a leaf The length of a leaf on a tree is...Ch. 13.2 - Prob. 26ECh. 13.2 - Prob. 30ECh. 13.2 - Prob. 31ECh. 13.2 - Prob. 33ECh. 13.2 - Prob. 34ECh. 13.2 - Prob. 35ECh. 13.2 - Prob. 36ECh. 13.2 - Prob. 37ECh. 13.2 - Prob. 39ECh. 13.2 - Prob. 40ECh. 13.3 - YOUR TURN Repeat Example 2 for a flashlight...Ch. 13.3 - Prob. 1ECh. 13.3 - Prob. 2ECh. 13.3 - Prob. 3ECh. 13.3 - Prob. 4ECh. 13.3 - Prob. 5ECh. 13.3 - Prob. 6ECh. 13.3 - Prob. 7ECh. 13.3 - Prob. 8ECh. 13.3 - Prob. 9ECh. 13.3 - Prob. 10ECh. 13.3 - Prob. 11ECh. 13.3 - Prob. 12ECh. 13.3 - Prob. 13ECh. 13.3 - Prob. 14ECh. 13.3 - Describe the standard normal distribution. What...Ch. 13.3 - Prob. 16ECh. 13.3 - Suppose a random variable X has the Poisson...Ch. 13.3 - Prob. 19ECh. 13.3 - Prob. 20ECh. 13.3 - Prob. 21ECh. 13.3 - Prob. 22ECh. 13.3 - Prob. 23ECh. 13.3 - Find each of the following probabilities for the...Ch. 13.3 - Prob. 25ECh. 13.3 - Prob. 26ECh. 13.3 - Prob. 27ECh. 13.3 - Prob. 28ECh. 13.3 - Prob. 30ECh. 13.3 - Determine the cumulative distribution function for...Ch. 13.3 - Prob. 36ECh. 13.3 - Prob. 37ECh. 13.3 - Prob. 38ECh. 13.3 - Prob. 39ECh. 13.3 - Pygmy Height The average height of a member of a...Ch. 13.3 - Prob. 41ECh. 13.3 - Prob. 42ECh. 13.3 - Prob. 43ECh. 13.3 - Prob. 44ECh. 13.3 - Prob. 45ECh. 13.3 - Prob. 46ECh. 13.3 - Prob. 47ECh. 13.3 - Prob. 48ECh. 13.3 - Prob. 49ECh. 13.3 - Earthquakes The proportion of the times in days...Ch. 13.3 - Prob. 51ECh. 13.3 - Prob. 52ECh. 13.3 - Prob. 53ECh. 13.3 - Prob. 54ECh. 13.3 - Prob. 55ECh. 13.3 - Printer Failure The lifetime of a printer costing...Ch. 13.3 - Electronic Device The time to failure of a...Ch. 13.CR - Prob. 1CRCh. 13.CR - Prob. 3CRCh. 13.CR - Prob. 4CRCh. 13.CR - Prob. 5CRCh. 13.CR - Prob. 6CRCh. 13.CR - Prob. 7CRCh. 13.CR - Prob. 8CRCh. 13.CR - Prob. 9CRCh. 13.CR - Prob. 10CRCh. 13.CR - Prob. 11CRCh. 13.CR - Prob. 12CRCh. 13.CR - Prob. 13CRCh. 13.CR - Prob. 14CRCh. 13.CR - Prob. 15CRCh. 13.CR - Prob. 16CRCh. 13.CR - Prob. 17CRCh. 13.CR - Prob. 18CRCh. 13.CR - Prob. 19CRCh. 13.CR - Prob. 20CRCh. 13.CR - Prob. 21CRCh. 13.CR - Prob. 22CRCh. 13.CR - Prob. 23CRCh. 13.CR - Prob. 24CRCh. 13.CR - Prob. 25CRCh. 13.CR - Prob. 26CRCh. 13.CR - Prob. 27CRCh. 13.CR - Prob. 28CRCh. 13.CR - Prob. 29CRCh. 13.CR - Prob. 30CRCh. 13.CR - Prob. 31CRCh. 13.CR - Prob. 32CRCh. 13.CR - Prob. 33CRCh. 13.CR - Prob. 34CRCh. 13.CR - Prob. 35CRCh. 13.CR - Prob. 36CRCh. 13.CR - Prob. 39CRCh. 13.CR - Prob. 40CRCh. 13.CR - Prob. 41CRCh. 13.CR - Prob. 42CRCh. 13.CR - Prob. 43CRCh. 13.CR - Prob. 44CRCh. 13.CR - Prob. 45CRCh. 13.CR - Prob. 46CRCh. 13.CR - Prob. 47CRCh. 13.CR - Prob. 48CRCh. 13.CR - Prob. 52CRCh. 13.CR - Prob. 54CRCh. 13.CR - Prob. 55CRCh. 13.CR - Prob. 56CRCh. 13.CR - Prob. 57CRCh. 13.CR - Prob. 58CRCh. 13.CR - Prob. 59CRCh. 13.CR - Prob. 60CRCh. 13.CR - Prob. 61CRCh. 13.CR - Yeast cells The famous statistician William...Ch. 13.CR - Prob. 65CRCh. 13.CR - Equipment Insurance A piece of equipment is being...
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