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

94.3 %94.3%

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

enter your response here.

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

Data

Sample size

3

Probability of an event of interest

0.9090.909

Parameters

Mean

2.7272.727

Variance

0.24820.2482

Standard Deviation

0.49820.4982

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

0.00080.0008

0.00080.0008

0.0000

0.99930.9993

1.00011.0001

1

0.02260.0226

0.02340.0234

0.00080.0008

0.97670.9767

0.99930.9993

2

0.22560.2256

0.24900.2490

0.02340.0234

0.75110.7511

0.97670.9767

3

0.75110.7511

1.00011.0001

0.24900.2490

0.0000

0.75110.7511

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