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miskamm [114]
2 years ago
15

Bluesky air has the best on-time arrival rate with 80% of its flights arriving on time. a test is conducted by randomly selectin

g 16 bluesky air flights and observing whether they arrive on time. what is the probability that 2 flights of bluesky air arrive late? (please carry answers to at least six decimal places in intermediate steps. give your final answer to the nearest three decimal places).
Mathematics
1 answer:
MakcuM [25]2 years ago
3 0
I would use binomial distribution to answer this, since a flight being late is an independent event.
So X ~ B(16, 0.2)
The above line states that the probability of X relates to the binomial distribution with 16 trials (the 16 flights) and a 20% (0.2) chance of "success" (in this case the "success" is beimg late, which is weird because being late is not a very good thing, but the question is about being late so allow it)
So the probability of 2 flights arriving late is P(X=2) = 16C2 × 0.2^2 × 0.8^14
(The formula is basically, trialsCsuccesses × (chance of success)^(number of successes) × (chance of failure)^(total trials - successes)

The calculation will give you a probability of 0.211. And that is it :)

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We need a sample size of at least 719

Step-by-step explanation:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

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Now, find the margin of error M as such

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This is at least n, in which n is found when M = 0.3, \sigma = 4.103. So

M = z*\frac{\sigma}{\sqrt{n}}

0.3 = 1.96*\frac{4.103}{\sqrt{n}}

0.3\sqrt{n} = 1.96*4.103

\sqrt{n} = \frac{1.96*4.103}{0.3}

(\sqrt{n})^{2} = (\frac{1.96*4.103}{0.3})^{2}

n = 718.57

Rouding up

We need a sample size of at least 719

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To find the value of x we can take the two, CD or DE and set them equal to CE.

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