Question

In: Statistics and Probability

A​ government's department of transportation reported that in​ 2009, airline A led all domestic airlines in​...

A​ government's department of transportation reported that in​ 2009, airline A led all domestic airlines in​ on-time arrivals for domestic​ flights, with a rate of 82.9%.

Complete parts a through e below.

a.What is the probability that in the next six​ flights, exactly four flights will be on​ time?

b. What is the probability that in the next six​ flights, two or fewer will be on​ time?

.c. What is the probability that in the next six​ flights, at least four flights will be on​ time?

d. d. What are the mean and standard deviation for this​ distribution?

Solutions

Expert Solution

A​ government's department of transportation reported that in​ 2009, airline A led all domestic airlines in​ on-time arrivals for domestic​ flights, with a rate of 82.9%.

Complete parts a through e below.

Binomial distribution used.

n=6, p=0.829

a.What is the probability that in the next six​ flights, exactly four flights will be on​ time?

P( x=4) =0.2072

Excel function used: =BINOM.DIST(4,6,0.829,FALSE)

b. What is the probability that in the next six​ flights, two or fewer will be on​ time?

P( x ≤2) =P( x=0)+P(x=1)+P( x=2)

=0.0000+0.0007+0.0088

=0.0095

.c. What is the probability that in the next six​ flights, at least four flights will be on​ time?

P( x≥4) =P( x=4)+P( x=5)+P(x=6)

=0.2072+0.4017+0.3246

=0.9335

d. d. What are the mean and standard deviation for this​ distribution?

Expectation = np = 4.974
Variance = np(1 - p) = 0.850554

Mean = 4.974, sd=0.9223

Binomial Probabilities

Data

Sample size

6

Probability of an event of interest

0.829

Statistics

Mean

4.974

Variance

0.8506

Standard deviation

0.9223

Binomial Probabilities Table

X

P(X)

0

0.0000

1

0.0007

2

0.0088

3

0.0570

4

0.2072

5

0.4017

6

0.3246

orchestra answered 1 year ago
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