Download Normal Distribution Calculations

12/1/2014
Warm-Up
The probability that a person owns and I-phone is 0.64.
What is the probability that in a random group of 10 people, at least 7
own an I-phone?
What is the probability that in a random group of 8 people, exactly 12
own their own phone.
In a group of 20, what is the expected number & standard deviation
that own an I-phone?
What is the probability that if we begin asking random people if they
have an I-phone we don’t find an I-phone owner until the 5th person
asked?
After HW
Lesson 2 Warm-up…(1-12)
Normal Distribution
Calculations
When Tiger Woods hits his driver, the distance the ball travels
follows a Normal Distribution with mean 304 yards and standard
deviation 8 yards. What percent of Tiger’s drives travel at least
290 yards?
Let x = the distance Tiger’s ball
travels and it has a distribution
N(304, 8). We want P(x ≥ 290).
290 − 304 

P ( x ≥ 290) = P z ≥
 = P ( z ≥ −1.75) = 1 − 0.0401 = 0.9599
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

About 96% of Tigers drives travel at least 290 yards.
Scores for a test have a mean of 100 and standard
deviation of 15. Find the probability that a score is
below 112.
Every month, American households generate an
average of 28 pounds of newspaper for garbage or
recycling. Assume σ=2 pounds. If a household is
selected at random, find the probability that it
generates between 27 and 31 pounds per month.
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12/1/2014
An exclusive college desires to accept only the top 10% of all
graduating seniors based on the results of a national placement
test. This test has a mean of 500 and a standard deviation of 100.
Find the cutoff score for the exam.
In the 2008 Wimbledon tennis tournament, Rafael Nadal averaged
115 miles per hour (mph) on his first serves. Assume that the
distribution of his first serve speeds is Normal with a mean of 115
mph and a standard deviation of 6 mph. About what proportion of
his first serves would you expect to exceed 120 mph?
According to http://www.cdc.gov/growthcharts/, the heights of 3
year old females are approximately Normally distributed with a
mean of 94.5 cm and a standard deviation of 4 cm. What is the
For a medical study a researcher wishes to select people in the
middle 60% of the population based on blood pressure. If the
mean systolic blood pressure is 120 and the standard deviation is
8, find the upper and lower reading that would qualify a person to
be in the study.
What percent of Rafael Nadal’s first serves are
between 100 and 110 mph? N(115, 6)
Classwork
third quartile of this distribution?
Lesson 2 Warm-Up: (11-14)
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12/1/2014
Homework
Worksheet
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