C In Problems 17 – 20 , use a graphing calculator to graph the normal probability density function f ( x ) = 1 σ 2 π e − ( x − μ ) 2 / 2 σ 2 that has the given mean μ and standard deviation σ. 17. μ = 0, σ = 1
C In Problems 17 – 20 , use a graphing calculator to graph the normal probability density function f ( x ) = 1 σ 2 π e − ( x − μ ) 2 / 2 σ 2 that has the given mean μ and standard deviation σ. 17. μ = 0, σ = 1
Solution Summary: The author illustrates the graph of the normal probability distribution with f(x)=1sigma.
West Virginia has one of the highest divorce rates in the nation, with an annual rate of approximately 5 divorces per 1000 people (Centers for Disease Control and Prevention website, January 12, 2012). The Marital Counseling Center, Inc. (MCC) thinks that the high divorce rate in the state may require them to hire additional staff.
Working with a consultant, the management of MCC has developed the following probability distribution for x = the number of new clients for marriage counseling for the next year.
Excel File: data05-19.xls
10
20
f(x)
.05
.10
11
30
40
50
60
.10
.20
.35
.20
a. Is this probability distribution valid?
Yes
Explain.
greater than or equal to 0
f(x)
Σf(x)
equal to 1
b. What is the probability MCC will obtain more than 30 new clients (to 2 decimals)?
c. What is the probability MCC will obtain fewer than 20 new clients (to 2 decimals)?
d. Compute the expected value and variance of x.
Expected value
Variance
clients per year
squared clients per year
Use Variation of Parameters to solve
Use the method of washers to find the volume of the solid that is obtained
when the region between the graphs f(x) = √√2 and g(x) = secx over the
interval ≤x≤ is rotated about the x-axis.
Chapter 6 Solutions
Calculus for Business, Economics, Life Sciences, and Social Sciences - Boston U.
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