According to an ? airline, flights on a certain route are on time 85 8 5 ? % of

Question

According to an? airline, flights on a certain route are on time 8585?% of the time. Suppose 1010 flights are randomly selected and the number of on time flights is recorded. Use technology to find the probabilities. Use the Tech Help button for further assistance. ?(a) Determine whether this is a binomial experiment. ?(b) Find and interpret the probability that exactly 88 flights are on time. ?(c) Find and interpret the probability that at least 88 flights are on time. ?(d) Find and interpret the probability that fewer than 88 flights are on time. ?(e) Find and interpret the probability that between 66 and 88 ?flights, inclusive, are on time. According to an? airline, flights on a certain route are on time 8585?% of the time. Suppose 1010 flights are randomly selected and the number of on time flights is recorded. Use technology to find the probabilities. Use the Tech Help button for further assistance. 8585?% 1010 ?(a) Determine whether this is a binomial experiment. ?(b) Find and interpret the probability that exactly 88 flights are on time. 88 ?(c) Find and interpret the probability that at least 88 flights are on time. 88 ?(d) Find and interpret the probability that fewer than 88 flights are on time. 88 ?(e) Find and interpret the probability that between 66 and 88 ?flights, inclusive, are on time. 66 88

Explanation / Answer

Ans:

Given that

n=10,p=0.85

P(x=r)=10Cr*0.85r*(1-0.85)10-r

a)Yes,it is binomial distribution,as only two outcomes possible(whether on time or not) and independent trials.

b)

P(x=8)=10C8*0.858*0.152=0.2759

c)Use below table for calculations:

P(atleast 8)=P(x>=8)

=P(x=8)+P(x=9)+P(x=10)

=0.276+0.347+0.197

=0.820

d)P(x<8)=1-P(x>=8)=1-0.820=0.180

e)P(6<=x<=8)=P(x=6)+P(x=7)+P(x=8)

=0.040+0.130+0.276=0.446

x p(x) 0 0.000 1 0.000 2 0.000 3 0.000 4 0.001 5 0.008 6 0.040 7 0.130 8 0.276 9 0.347 10 0.197

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