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Math  /  Data & Statistics

QuestionYour flight has been delayed: At Denver International Airport, 82%82 \% of recent flights have arrived on time. A sample of 11 flights is studied.
Round the probabilities to at least four decimal places.
Part 1 of 4 (a) Find the probability that all 11 of the flights were on time.

Studdy Solution

STEP 1

1. The probability of a single flight arriving on time is 0.82 0.82 .
2. The number of flights in the sample is 11.
3. Each flight's arrival time is an independent event.

STEP 2

1. Identify the probability of a single flight arriving on time.
2. Use the binomial probability formula to find the probability that all 11 flights were on time.

STEP 3

Identify the probability of a single flight arriving on time:
P(on time)=0.82 P(\text{on time}) = 0.82

STEP 4

Since we want all 11 flights to be on time, we use the formula for the probability of all independent events occurring:
P(all 11 on time)=(P(on time))11 P(\text{all 11 on time}) = (P(\text{on time}))^{11}

STEP 5

Substitute the probability of a single flight being on time into the formula:
P(all 11 on time)=(0.82)11 P(\text{all 11 on time}) = (0.82)^{11}

STEP 6

Calculate the probability:
P(all 11 on time)=0.8211≈0.1159 P(\text{all 11 on time}) = 0.82^{11} \approx 0.1159
The probability that all 11 flights were on time is approximately:
0.1159 \boxed{0.1159}

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