# Binomial random variable

I need to show all work such as formula commands.

Label the following variables as discrete or continuous and explain why it is so, then verify at least one of the other postings.

a. The number of new accounts established by a salesperson in a year.

b. The time between customer arrivals to a bank ATM

c. The number of customers in Big Nick?s barber shop

d. The amount of fuel in your car?s gas tank

e. The number of minorities on a jury

f. The outside temperature today

g. A person?s height

h. The amount of money a person is carrying

i. Your age

Team Five:

A marketing poll revealed that 45% of Americans say they that they have dinner regularly as a family. You randomly choose 10 American families and ask if they regularly have dinner together as a family.

1. Does this situation meet the binomial requirements? Why or why not? Address the five characteristics in the Key Points.

2. What is the random variable in this problem? i.e., what does X represent and what values can it have?)

3. What is the probability that exactly 4 have regular family dinner?

4. What is the probability that 5 or fewer have regular family dinner?

5. What is the probability that at least 2 have regular family dinner?

6. What is the probability that at most 5 have regular family dinner?

7. What is the mean number of adults out of a sample of 10 that you would expect to have regular family dinner? What is the standard deviation of the distribution?

#### Solution Preview

Please see attached file.

Discrete Variable : Discrete variable is one that cannot take on all values within the limits of the variable.

Continuous Variable : Continuous variable is one for which, within the limits the variable ranges, any value is possible.

Label the following variables as discrete or continuous and explain why it is so, then verify at least one of the other postings.

a. The number of new accounts established by a salesperson in a year.

Answer

The number of accounts established by a sales person can take values

{0,1,2,?.. } So it is discrete

b. The time between customer arrivals to a bank ATM

Answer

The time between customer arrivals to a bank ATM can take value in the interval

(0,â?? ) So it is a continuous variable

c. The number of customers in Big Nick?s barber shop

Answer

The number of customers in Big Nick?s barber shop can take values

{0,1,2,?.. } So it is discrete ...

#### Solution Summary

The solution gives the complete steps of calculating probability of a binomial random variable. Step by step solution is given with interpretations.