Find the following:
X
Y
3𝑥 − 𝑦
Mean St. Dev.
50
12
28
5
2𝑥 + 3𝑦 − 7
MORE BINOMIAL
USING CALCULATOR
Section 6.3B
You have a small business making and delivering box lunches. It costs you
$2.10 per lunch plus $75 for operating costs. If the number of lunches you
sell is shown below, find the expected cost for making and delivering the box
lunches as well as the standard deviation.
x= #
lunches
200
240
280
320
360
p(x)
0.15
0.17
0.28
0.32
0.08
The cost to rent a car is $45 per day and $.25 per mile. The
distributions for each are shown below. Find the expected
cost to rent a car and the standard deviation of the cost.
d=
#days
p(d)
1
2
3
4
5
6
0.13 0.18 0.22 0.31 0.09 0.07
Using the calculator to find binomial
probabilities.
• To find exactly 1 probability:
binompdf(n, p, x)
Press:
2nd Distribution
0 binompdf(n,p,x)
n – for number of trials
p – for given percent
x - # we want
A tourist bureau for a western state conducted a study, which
showed that 65% of the people who seek information about the
state actually come for a visit. The office receives 15 requests for
information on the state. Find the probability that exactly 10 visit.
• Binompdf(15, 0.65, 10)
• You should get 0.2123 or 21.2%
Remember: PDF is for exactly
To accumulate probabilities – adding
more than one- we use binomcdf.
• It accumulates starting with x = 0 up to the value you
want.
• It’s under 2nd distribution
A binomcdf (n, p, x)
A survey found that 30% of teens get spending money from
part time jobs. If 5 teens are selected at random find the
probability that at most 3 of them have part time jobs.
x
p(x)
0
0.16807
1
0.36015
2
0.3087
3
0.1323
4
0.02835
5
0.00243
0.96922
On the calculator:
Binomcdf(5, 0.30,3)
A survey found that 30% of teens get spending money from part
time jobs. If 5 teens are selected at random find the probability
that at least 3 of them have part time jobs.
x
p(x)
0
0.16807
On the calculator:
1
0.36015
Binomcdf(5, 0.30,2)= 0.83692
2
0.3087
3
0.1323
4
0.02835
5
0.00243
0.16308
1 - Binomcdf(5, 0.30,2) = 0.16308
To do the bottom of the list:
• You accumulate the top part of the distribution.
• Subtract from 1.
A survey found that 30% of teens get spending money from part
time jobs. If 5 teens are selected at random find the probability
that more than 3 of them have part time jobs.
x
p(x)
0
0.16807
1
0.36015
On the calculator:
Binomcdf(5, 0.30,2)= 0.96922
2
0.3087
3
0.1323
4
0.02835
5
0.00243
0.03078
1 - Binomcdf(5, 0.30,3) = 0.03078
Tim did not study for his quiz with 5 multiple choice (A, B, C, D)
questions.
Hint: Probability of correct choice is ¼ = 0.25!
• What is the probability that he got exactly 3 correct?
• What is the probability that he got at most 2 correct?
• What is the probability that he got more than 3
correct?
A certain type of penicillin will cause a skin rash in
35% of the patients receiving it.
• If the penicillin is given to a random sample of 15
patients what is the probability that at least 7 will
have a skin rash?
• If it is given to a random sample of 9 patients, what is
the probability that at least one will have a skin rash?
• If it is given to a random sample of 12 patients, what
is the probability that exactly 5 will have a skin rash?
The probability that a person gets a job within a
month of graduating from college is 78%.
• Find the probability that in a group of 8 recent graduates,
more than 6 found a job.
• Find the probability that in a group of 12, at least 9 found
a job.
Homework
*Worksheet