# Using Binomial Probability Distribution

1

Pan Thai Restaurant offers 5% discount if the customer pays in cash instead of paying by a credit card. Past evidence indicates that 30% of all customers pay in cash. During a day period 120 customers buy gasoline at this station.

(a) What is the probability that at least 50 customers pay in cash?

(b) What is the probability that no more than 15 customers pay in cash?

(c) What is the probability that more than 20 and less than 40 customers pay in cash?

(d) Using the choices listed below, what type of discrete probability distribution is this an example of and why?

Continuous probability distribution

Poisson probability distribution

Binomial probability distribution

Hyper geometric probability distribution

2

The following table gives results of the 2008 Business Survey question, "Are business income taxes too high, about right, or too low?" categorized by the type of companies:

Type Too High About Right Too Low Total

Public 294 12

Private 116 23 1624

Total 1779 186

a. Complete the table.

Public: About Right-

Public: Total-

Private: Too High-

Total: Too Low-

Total: Total

b. How many were surveyed?

c. How many public companies respond that taxes are about right?

d. How many private companies respond that taxes are too high?

e. How many private companies are in the survey?

f. How many companies respond that taxes are too high are public companies?

g. Rewrite the event stated in part (f), using the expression "given that."

h. Find the probability of the outcome in parts (f) and (g).

i. Find the probability that a private company respond that taxes are about right.

#### Solution Preview

1

Pan Thai Restaurant offers 5% discount if the customer pays in cash instead of paying by a credit card. Past evidence indicates that 30% of all customers pay in cash. During a day period 120 customers buy gasoline at this station.

(a) What is the probability that at least 50 customers pay in cash?

This is a binomial probability: n=120, x=50, p=0.30.

P(x>=50) ==1-P(x<=49)=1-BINOM.DIST(49,120,0.3,TRUE)= 0.004354

(Binom.dist is a function in excel, "true" means cumulative).

(b) What is the probability that no more than 15 customers pay in cash?

P(x<=15)=binom.dist(15,120,0.3,true)= 5.4195E-06

(c) What is the probability that more than 20 and less than 40 customers pay in cash?

P(20<x<40)=P(x<=39)-P(x<=20)=binom.dist(39,120,0.3,true)-binom.dist(20,120,0.3,true)= 0.7586468

(d) Using the choices listed below, what type of discrete ...

#### Solution Summary

The expert uses binomial probability distributions.