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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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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The time spent (in days) waiting for a
kidney transplant for people ages 35-49 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?
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.
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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.
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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
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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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?
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?