Download 5-2B Lecture

Section 5 – 2B:
It is not always necessary to create the entire table
to find the answer to a problem.
Example 1
The NRA reports that 23% of all men own a shotgun. If you survey 45 men what is the probability
that exactly 10 ot those 45 men surveyed will own a shotgun.
DO NOT complete a table for all the values of x from 0 to 10
You only need to find P(10)
We surveyed 45 men so n = 45
Success is defined as owning a shotgun and failure is defined as not owning one.
The probability of any one man owning a shotgun is 23% so p = .23
If 23% of men do own a shotgun then 77% of men do not own one. q = .77
We want to find out the probability that exactly 10 of the 45 men surveyed own a shotgun so x = 10
If we want 10 successes then the number of failures is 35.
P(0) =
45C10
• .2310 • .7735 = .14
Conclusion: if you survey 45 men about shotgun ownership there is a 14% chance that exactly 10
of them will say they own one.
Section 5 – 2B Lecture
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© 2012 Eitel
Example 2
The procedure is to spin the spinner 5 times. Find the probability that the
expected number of times you will land on blue is less than 2 out of 5
We spin 5 times so n = 5
Success is defined as landing on blue and failure is defined as not landing on blue.
The probability of landing on blue is 1/ 4 so p = .25
Failure is NOT landing on blue. The probability of NOT landing on blue is 3/ 4 so q = .75
We want to find out the probability that exactly 10 of the 45 men surveyed own a shotgun so x = 10
To find P( x < 2 Blue) just compute the totals of P(0) and P(1)
If we want 0 successes out of 5 then the number of failures is 5.
P(0 Blues) = 5 C0 • .250 • .755 = .24
If we want 1 successes out of 5 then the number of failures is 4
P(1 Blue) = 5 C1 • .251 • .754 = .40
P( x < 2 Blue) = P(0) + P(1) = .64
Conclusion: if you spin the spinner 5 times there is a 64% chance that the number of times it lands
on blue less then 2 times.
Section 5 – 2B Lecture
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© 2012 Eitel
Note: The answers in your book are found by rounding each separate P(x) to 2 decimal places and
then adding them together. This may not be as accurate as keeping 4 decimal places for each
P(x) and then adding the 4 decimal place numbers and then rounding the final answer. It
is better to avoid rounding off values to 2 decimal places until the final step.
Example of rounding before adding the P(x) values
or adding the 4 place P(x) values and then rounding
Each P(x) was rounded to 2 decimal
places first and then added.
Each P(x) was computed to 4 decimal
places and then added. That final total
was then rounded.
If the question asks what is the
probability that the number of blue spins
is less than 2 out of the 5 spins
P(x < 2)
you would calculate P(0) + P(1)
If the question asks what is the
probability that that the number of blue
spins is less than 2 out of the 5 spins
P(x < 2)
you would calculate P(0) + P(1)
P(0) = 5 C0 • .25 0 • .755 = .24
P(0) = 5 C0 • .25 0 • .755 = .2373
P(1) = 5 C1 • .251 • .754 = ..40
P(1) = 5 C1 • .251 • .754 = .3955
P(x < 2) = P(0) + P(1)
P(x < 2) = P(0) + P(1)
P(x < 2) ≈ .64
P(x < 2) ≈ .63
Section 5 – 2B Lecture
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© 2012 Eitel
Example 3
The Gardner Group reports that 94% of American boys age 13 to 19 play video games more than
8 hours a week. If you survey 60 American boys age 3 to 19 what is the probability that more
than 57 of those 60 boys surveyed will have play video games more than 8 hours a week.
We surveyed 60 boys so n = 60
Success is defined as playing a video game more than 8 hours a week.
Failure is defined as not having playing a video game more than 8 hours a week.
The probability of any one teenager playing a video game is 94% p = .94
If 94% of teenage boys have played a video game then 6% of them have not. q = .06
We want to find out the probability that more than 57 of the 60 boys surveyed play so x > 57
We need to find P(58) + P(59) + P(60)
P(58) = 60C 58 • .94 58 • .062 = .1761
P(59) =
60C 59 •
.94 59 • .061 = .0935
P(60) =
60C 60 •
.94 60 • .060 = .0244
P(x > 57) = P(58) + P(59) + P(60) ≈ .29
Conclusion: if you survey 60 American boys age 13 to 19 about video game playing there is a
29 % chance that more than 57 of them will say they have played a video game.
Note: If you had rounded each P(x) and then added the values you would have still gotten the same
answer of
P(x > 57) = P(58) + P(59) + P(60) = .18 + .09 + .02 ≈ .29
It is better to avoid rounding off values to 2 decimal places until the final step but in some cases
the answer will be the same in either case. The answers in your book are found by rounding each
separate P(x) to 2 decimal places and then adding them together.
Section 5 – 2B Lecture
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© 2012 Eitel