Question

Example #1:The director of admissions for a small private university collected data on past admissions and summarized the data in the table.

Topics: Characteristics of General Discrete Probability Distribution

Using Discrete Probability Distribution

admissions: 1000,1200,1500

probability: 0.6,0.3,0.1

What is the expected number of admissions for the Fall semester?

What is the variance?

what is the standard deviation?

Example 2: A movie theatre uses teams of three people to work the concession stand each evening. There are seven employees trained and available to work concessions. How many different teams of three can be scheduled to work the concession stand? Topic: Counting Rule for Combinations

Example 3: Suppose a small airline has five flights each day between Birmingham and Orlando. Also, suppose the probability that any of the five flights arrives late is 20%. Topic Binomial Probability Distribution

What is the probability that none of the five flights arrives late?

What is the probability that exactly one of the five flights arrives late?

What is the probability that one or more of the five flights arrive late?

Please show me how to do these problems using an HP 10b11+ calculator. Again using an HP 10b11+ calculator

Answer 1

1) The probability distribution of past admissions is

0.6, 1000 P(X = x) = {0.3, 1200 0.1, 1500

The expected value is

E(X) = xP(X = x) E(X) = 1000(0.6) + 1200(0.3) + 1500(0.1) E(X) = 1110

Also,

E(X2) = x?P(X = x) E(X?) = 1000P(0.6) + 1200²(0.3) + 1500?(0.1) E(X) = 1257000

Variance is

Var(X) = E(X) - E(X)2 Var(x) = 1257000 - 11102 Var(x) = 24900

2)The number of different teams of three can be scheduled to work the concession stand is

() = 35

3) The probability that none of the five flights arrives late is

(1 -0.25 = 0.32768

The probability that exactly one of the five flights arrives late is

(0.2(1 – 0.2)4 = 0.4096

The probability that one or more of the five flights arrive late is

1-(1-0.2)= = 0.67232