The May 26, 2009, USA Today Snapshot \"Overcoming Identity Theft\" reported the

Question

The May 26, 2009, USA Today Snapshot "Overcoming Identity Theft" reported the results from a poll of identity theft victims. According to the source, Affinion Security Center, 20% of the victims stated that it took "one week to one month" to recover from identity theft. A group of 14 identity theft victims are randomly selected in your hometown.

A) What is the probability none of them were able to recover from the theft in one week to one month?

B) What is the probability that exactly 3 were able to recover from the theft in one week to one month?

C) What is the probability that at least 5 were able to recover from the theft in one week to one month?

D) What is the probability that no more than 4 were able to recover from the theft in one week to one month?

Explanation / Answer

The May 26, 2009, USA Today Snapshot "Overcoming Identity Theft" reported the results from a poll of identity theft victims. According to the source, Affinion Security Center, 20% of the victims stated that it took "one week to one month" to recover from identity theft. A group of 14 identity theft victims are randomly selected in your hometown.

Binomial distribution used

n=14

p=0.2

A) What is the probability none of them were able to recover from the theft in one week to one month?

P( x=0)=0.044

B) What is the probability that exactly 3 were able to recover from the theft in one week to one month?

P( x=3) = 0.2501

C) What is the probability that at least 5 were able to recover from the theft in one week to one month?

P( x >=5) = 0.1298

D) What is the probability that no more than 4 were able to recover from the theft in one week to one month?

P( x <=4) = 0.8702

Data

Sample size

14

Probability of an event of interest

0.2

Statistics

Mean

2.8

Variance

2.2400

Standard deviation

1.4967

Binomial Probabilities Table

X

P(X)

P(<=X)

P(<X)

P(>X)

P(>=X)

0

0.0440

0.0440

0.0000

0.9560

1.0000

1

0.1539

0.1979

0.0440

0.8021

0.9560

2

0.2501

0.4481

0.1979

0.5519

0.8021

3

0.2501

0.6982

0.4481

0.3018

0.5519

4

0.1720

0.8702

0.6982

0.1298

0.3018

5

0.0860

0.9561

0.8702

0.0439

0.1298

6

0.0322

0.9884

0.9561

0.0116

0.0439

7

0.0092

0.9976

0.9884

0.0024

0.0116

8

0.0020

0.9996

0.9976

0.0004

0.0024

9

0.0003

1.0000

0.9996

0.0000

0.0004

10

0.0000

1.0000

1.0000

0.0000

0.0000

11

0.0000

1.0000

1.0000

0.0000

0.0000

12

0.0000

1.0000

1.0000

0.0000

0.0000

13

0.0000

1.0000

1.0000

0.0000

0.0000

14

0.0000

1.0000

1.0000

0.0000

0.0000

Data

Sample size

14

Probability of an event of interest

0.2

Statistics

Mean

2.8

Variance

2.2400

Standard deviation

1.4967

Binomial Probabilities Table

X

P(X)

P(<=X)

P(<X)

P(>X)

P(>=X)

0

0.0440

0.0440

0.0000

0.9560

1.0000

1

0.1539

0.1979

0.0440

0.8021

0.9560

2

0.2501

0.4481

0.1979

0.5519

0.8021

3

0.2501

0.6982

0.4481

0.3018

0.5519

4

0.1720

0.8702

0.6982

0.1298

0.3018

5

0.0860

0.9561

0.8702

0.0439

0.1298

6

0.0322

0.9884

0.9561

0.0116

0.0439

7

0.0092

0.9976

0.9884

0.0024

0.0116

8

0.0020

0.9996

0.9976

0.0004

0.0024

9

0.0003

1.0000

0.9996

0.0000

0.0004

10

0.0000

1.0000

1.0000

0.0000

0.0000

11

0.0000

1.0000

1.0000

0.0000

0.0000

12

0.0000

1.0000

1.0000

0.0000

0.0000

13

0.0000

1.0000

1.0000

0.0000

0.0000

14

0.0000

1.0000

1.0000

0.0000

0.0000

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