According to an airline, a particular flight is on time 85% of the time. Suppose

Question

According to an airline, a particular flight is on time 85% of the time. Suppose 10 flights are randomly selected and the number of on time flights is recorded. Use technology to find the probabilities.

(a) Determine whether this is a binomial exeperiment.

(b) Find and interpret the probability that exactly 8 flights are on time.

(c) Find and interpret the probability that at least 8 flights are on time.

(d) Find and interpret the probability that fewer than 8 flights are on time.

(e) Find and interpret the probability that between 6 and 8 flights, inclusive are on time.

Round to four decimal places.

Explanation / Answer

(a) Determine whether this is a binomial exeperiment.

All requirement are satisfied.

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(b) Find and interpret the probability that exactly 8 flights are on time.

Given X~Binomial(n=10, p=0.85)

P(X=x)=10Cx*(0.85^x)*(0.15^(10-x))

So P(X=8) =10C8*(0.85^8)*(0.15^(10-8)) =0.2759

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(c) Find and interpret the probability that at least 8 flights are on time.

P(X>=8) = P(X=8)+P(X=9)+P(X=10)

=10C8*(0.85^8)*(0.15^(10-8))+..+10C10*(0.85^10)*(0.15^(10-10))

=0.8202

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(d) Find and interpret the probability that fewer than 8 flights are on time.

P(X<8)= P(X=0)+P(X=1)+...+P(X=7)

=10C0*(0.85^0)*(0.15^(10-0))+....+10C7*(0.85^7)*(0.15^(10-7))

=0.1798

The probability is not low

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(e) Find and interpret the probability that between 6 and 8 flights, inclusive are on time.

P(6<=X<=8) = P(X=6)+P(X=7)+P(X=8)

=10C6*(0.85^6)*(0.15^(10-6))+..+10C8*(0.85^8)*(0.15^(10-8))

=0.4458

The probability is not low

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