Transcript MATH 1410/5.5 pp

Normal Approximations to
Binomial Distributions

TWO conditions:
np > 5
and
nq > 5
If conditions are met, then the random
variable x is normally distributed.

n = 15, p = 0.70, q = 0.30

n = 20, p = 0.65, q = 0.35


A survey of US adults found that 63% would
want to donate their organs if they died in a
accident. You randomly select 20 adults and
ask if they would donate their organs in the
same situation.
A survey of US adults found that 19% are
happy with their current employer. You
randomly select 30 adults and ask them about
this.



Binomial distributions are DISCRETE,
but the normal distribution is
CONTINUOUS.
The binomial probability formulas from
CH 4 are for exact probabilities. i.e.,
P(X = 4)
To adjust for continuity, move 0.5 units
to the left and right of the midpoint.
This allows you to include all x-values
in the interval. i.e., P(3.5 < X < 4.5)



1. The probability if getting between 39
and 77 successes, inclusive.
2. The probability of getting at least 80
successes.
3. The probability of getting at most 50
successes.
1.
2.
3.
4.
5.
6.
Find n, p, and q
Is np > 5? Is nq > 5?
Find µ and σ
Correct for Continuity (+ 0.5)
Find z
Use standard normal table to finish
A survey of US adults ages 50-64 found
that 70% use the Internet. You randomly
select 80 adults ages 50-64 and ask them if
they use the Internet.
 A. Find the prob. that at least 70 people
say they use the Internet.
 B. Find the prob. that exactly 50 people
say they use the internet.
 C. Find the prob. that more than 60
people say they use the internet.




26. About 34% of workers in the US are
college graduates. You randomly select
50 workers and ask them if they are a
college graduate.
A. Find the prob that exactly 12 workers
are college graduates.
B. Find the prob that more than 23
workers are college graduates.
C. Find the prob that at most 18
workers are college graduates.
D) A committee is looking for 30 working
college graduates to volunteer at a career
fair. The committee randomly selects 125
workers. What is the probability that
there will not be enough college
graduates?