To graph Problems 59-62, use a graphing calculator and refer to the normal probability distribution function with mean µ and standard deviation σ : f x = 1 σ 2 π e − x − μ 2 / 2 σ 2 Graph equation (1) with μ = 20 and (A) σ = 2 (B) σ = 4 Graph both in the same viewing window with Xmin = 0, Xmax = 40, Ymin = 0, and Ymax = 0 .2 .
To graph Problems 59-62, use a graphing calculator and refer to the normal probability distribution function with mean µ and standard deviation σ : f x = 1 σ 2 π e − x − μ 2 / 2 σ 2 Graph equation (1) with μ = 20 and (A) σ = 2 (B) σ = 4 Graph both in the same viewing window with Xmin = 0, Xmax = 40, Ymin = 0, and Ymax = 0 .2 .
Solution Summary: The author analyzes the equation of normal distribution. f(x)=1sigma
To graph Problems 59-62, use a graphing calculator and refer to the normal probability distribution function with mean
µ
and standard deviation
σ
:
f
x
=
1
σ
2
π
e
−
x
−
μ
2
/
2
σ
2
Graph equation (1) with
μ
=
20
and
(A)
σ
=
2
(B)
σ
=
4
Graph both in the same viewing window with
Xmin = 0, Xmax = 40, Ymin = 0, and Ymax = 0
.2
.
Definition Definition Probability of occurrence of a continuous random variable within a specified range. When the value of a random variable, Y, is evaluated at a point Y=y, then the probability distribution function gives the probability that Y will take a value less than or equal to y. The probability distribution function formula for random Variable Y following the normal distribution is: F(y) = P (Y ≤ y) The value of probability distribution function for random variable lies between 0 and 1.
Problem 1: A sample of 100 bulbs of brand A gave a
mean lifetime of 1200 has with a S.D. of 70hrs, while
another sample of 120 bulbs of brand B gave a mean
lifetime of 1150 has with a S.D. of 85hrs. Can we
calculate that brand A bulbs are superior to brand B
bulbs?
Question 4. The distribution of yield strength of steel bars in batch A is normal with mean 40,000 psi and the
coefficient of variation 10% while the yield strength of steel bars in batch B has a lognormal distribution with the
same mean and the same of coefficient of variations as those of batch A. If it is specified that the bars with the yield
strength less than 30,000 psi are considered defective and cannot be used for construction, which has higher
probability to be defective, a bar from batch A or B?
Problem 4 ,
| The daily revenue of an online retailer has mean 20 and variance 400.
(i) Find the lowest possible upper bound on the probability that the daily revenue exceeds 80.
(ii) Suppose the retailer is confident the daily revenue follows an exponential distribution. Can you
now make your answer to (i) more precise? If yes, provide it.
Chapter 10 Solutions
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
Mathematics with Applications In the Management, Natural and Social Sciences (11th Edition)
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