Download chAPTER four

Normal Distributions:
Finding Values
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Read the table (#4) in reverse
1. Make a quick sketch and shade the
area indicated.
2. Decide if the z-score is < or > zero.
3. Look in the BODY for the area given.
4. Read the row and column headings
to determine the z-score.
1. area = 0.9916
 2. P47
 3. 78.5% of the distribution is to
the right of the z-score.
 4. 25% of the distribution lies
between z and –z.
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Recall: z = x - µ
σ
If you know z, µ, and σ: just sub in
and solve for x.
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1. z = 1.62, µ = 13, σ = 0.39
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2. z = 0.45, µ = 24, σ = 0.7
Sketch the curve and shade the
probability.
 Find the z-score.
 Solve for x.
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34. The time spent (in days) waiting for
a kidney transplant for people ages 3549 in a recent year can be approximated
by a normal distribution with µ = 1674
days and σ = 212.5 days
A) What waiting time represents the
80th percentile?
B) What waiting time represents the
first quartile?
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36. The annual per capita consumption
of ice cream (in pounds) in the US can
be approximated by a normal
distribution. µ = 20.7 lb and σ = 4.2 lb.
A) What is the largest annual per capita
consumption of ice cream that can be in
the bottom 10% of consumption?
B) Between what two values does the
middle 80% of consumption lie?
Sampling Distributions
and the Central Limit
Theorem
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Sampling Distribution: the probability
distribution of a sample statistic that is
formed when samples of size n are repeatedly
taken from a population.
When sample MEANS are used, it’s called a
sampling distribution of sample means.
1.
2.
The mean of the sample means is equal
to the population mean.
The standard deviation of the sample
means is equal to the population
standard deviation divided by the
square root of the sample size. (This is
also called the standard error of the
mean.)
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#2. Given µ = 150 and σ = 25. Find the
mean and the standard deviation of a
sampling distribution of sample means
with sample size n = 100.
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1. If samples of size n, where n > 30, are
drawn from any population with mean µ and
standard deviation σ, then the sampling
distribution of sample means approximates a
normal distribution. The greater the sample
size n, the better the approximation.
2. If the population itself is normally
distributed, then the sampling distribution of
sample means is normally distributed for any
size n.
# 14. For a sample of n = 100, find the
probability of a sample mean being greater
than 24.3 if µ = 24 and σ = 1.25
# 26 The population mean annual salary for
flight attendants is $56,275. A random sample
of 48 flight attendants is selected from this
population. What is the probability that the
mean annual salary of the sample is less than
$56,100? Assume σ = $1800.
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# 38. A brake pad manufacturer claims its
brake pads will last for 38,000 miles. You
work for a consumer protection agency and
you are testing this manufacturer’s brake
pads. Assume the life spans of the brake
pads are normally distributed. You randomly
select 50 brake pads. In your tests, the mean
life of the brake pads is 37,650 miles. Assume
σ = 1000 miles.
A) What is the probability that the mean of
the sample is 37,650 miles or less?
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B) What do you think of the manufacturer’s
claim?
C) Would it be unusual to have an individual
brake pad last for 37,650 miles? Why or why
not?