Suppose that you and two friends go to a​ restaurant, which last month filled approximately

96.6 %96.6%

of the orders correctly. Complete parts​ (a) through​ (e) below.

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Click the icon to view the​ order-filling data for two other restaurants.

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Part 1

a. What is the probability that all three orders will be filled​ correctly?

The probability is

0.90140.9014.

​(Round to four decimal places as​ needed.)

Part 2

b. What is the probability that none of the three orders will be filled​ correctly?

The probability is

0.00100.0010.

​(Round to four decimal places as​ needed.) Probability of Correct Order at Restaurant B

Data

Sample size

3

Probability of an event of interest

0.8850.885

Parameters

Mean

2.6552.655

Variance

0.30530.3053

Standard Deviation

0.55250.5525

Binomial Probabilities Table

X

​P(X)

​P(less than or equals≤​X)

​P(less than<​X)

​P(greater than>​X)

​P(greater than or equals≥​X)

0

0.00150.0015

0.00150.0015

0.0000

0.99850.9985

1.00001.0000

1

0.03510.0351

0.03660.0366

0.00150.0015

0.96340.9634

0.99850.9985

2

0.27020.2702

0.30680.3068

0.03660.0366

0.69320.6932

0.96340.9634

3

0.69320.6932

1.00001.0000

0.30680.3068

0.0000

0.69320.6932

Probability of Correct Order at Restaurant C

Data

Sample size

3

Probability of an event of interest

0.8230.823

Parameters

Mean

2.4692.469

Variance

0.43700.4370

Standard Deviation

0.66110.6611

Binomial Probabilities Table

X

​P(X)

​P(less than or equals≤​X)

​P(less than<​X)

​P(greater than>​X)

​P(greater than or equals≥​X)

0

0.00550.0055

0.00550.0055

0.0000

0.99450.9945

1.00001.0000

1

0.07740.0774

0.08290.0829

0.00550.0055

0.91710.9171

0.99450.9945

2

0.35970.3597

0.44260.4426

0.08290.0829

0.55740.5574

0.91710.9171

3

0.55740.5574

1.00001.0000

0.44260.4426

0.0000

0.55740.5574

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