Find the following:   Mean St. Dev.X 50 12Y 28 5

3 𝑥− 𝑦 2 𝑥+3 𝑦−7

MORE BINOMIAL USING CALCULATORSection 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 1 2 3 4 5 6p(d) 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

1 0.36015

2 0.3087

3 0.1323

4 0.02835

5 0.00243

0.16308

On the calculator:

Binomcdf(5, 0.30,2)= 0.83692

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

2 0.3087

3 0.1323

4 0.02835

5 0.00243

0.03078

On the calculator:

Binomcdf(5, 0.30,2)= 0.96922

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