Question

According to a flight statistics​ website, in​ 2009, a certain airline had the highest percentage of​...

According to a flight statistics​ website, in​ 2009, a certain airline had the highest percentage of​ on-time flights in the airlines​ industry, which was 81.2​%. Assume this percentage still holds true for that airline. Use the normal approximation to the binomial distribution to complete parts a through c below. b. Determine the probability​ that, of the next 30 flights from this​ airline, exactly 27 flights will arrive on time.

Homework Answers

Answer #1

b)

n= 30 p= 0.8120
here mean of distribution=μ=np= 24.36
and standard deviation σ=sqrt(np(1-p))= 2.14
for normal distribution z score =(X-μ)/σx
therefore from normal approximation of binomial distribution and continuity correction:

probability​ that, of the next 30 flights from this​ airline, exactly 27 flights will arrive on time :

probability =P(26.5<X<27.5)=P((26.5-24.36)/2.14)<Z<(27.5-24.36)/2.14)=P(1<Z<1.47)=0.9292-0.8413=0.0879
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
According to a flight statistics​ website, in​ 2009, a certain airline had the highest percentage of​...
According to a flight statistics​ website, in​ 2009, a certain airline had the highest percentage of​ on-time flights in the airlines​ industry, which was 81.2​%. Assume this percentage still holds true for that airline. Use the normal approximation to the binomial distribution to complete parts a through c below. Determine the probability​ that, of the next 30 flights from this​ airline, less than 24 flights will arrive on time.
32.71% of Delta Airlines were never on time in 2016. Assume this percentage still holds true...
32.71% of Delta Airlines were never on time in 2016. Assume this percentage still holds true for airline. For the next 31 flights from Delta Airlines, use the normal approximation to the binominal distribution to answer the following questions. a) Find the probability that exactly 9 flights will arrive on time. b) Find the probability that fewer than 15 flights will arrive on time. c) Find the probability that 21, 22, or 23 flights will arrive on time.
According to the U.S. Bureau of Transportation Statistics, 20% of airline flights in the United States...
According to the U.S. Bureau of Transportation Statistics, 20% of airline flights in the United States failed to arrive on time in 2017. Airlines concentrated heavily to reduce this number for 2018. Suppose that in a recent random sample of 350 flights, 63 failed to arrive on time. Test at the 10% significance level whether the current percentage of all U.S. flights that fail to arrive on time decreased from 20%.C) Compute the Test Statistic D) Find the p-value (using...
A certain flight arrives on time 81 percent of the time. Suppose 122 flights are randomly...
A certain flight arrives on time 81 percent of the time. Suppose 122 flights are randomly selected. Use the normal approximation to the binomial to approximate the probability that ​(a) exactly 110 flights are on time. ​(b) at least 110 flights are on time. ​(c) fewer than 110 flights are on time. ​(d) between 110 and 111, inclusive are on time.
A certain flight arrives on time 83 percent of the time. Suppose 130 flights are randomly...
A certain flight arrives on time 83 percent of the time. Suppose 130 flights are randomly selected. Use the normal approximation to the binomial to approximate the probability that ​(a) exactly 117 flights are on time. ​(b) at least 117 flights are on time. ​(c) fewer than 96 flights are on time. ​(d) between 96 and 108​, inclusive are on time.
A certain flight arrives on time 85 percent of the time. Suppose 188 flights are randomly...
A certain flight arrives on time 85 percent of the time. Suppose 188 flights are randomly selected. Use the normal approximation to the binomial to approximate the probability that ​(a) exactly 160 flights are on time. ​(b) at least 160 flights are on time. ​(c) fewer than 155 flights are on time. ​(d) between 155 and 166​, inclusive are on time.
A certain flight arrives on time 90 percent of the time. Suppose 166 flights are randomly...
A certain flight arrives on time 90 percent of the time. Suppose 166 flights are randomly selected. Use the normal approximation to the binomial to approximate the probability that ​(a) exactly 146 flights are on time. ​(b) at least 146 flights are on time. ​(c) fewer than 139 flights are on time. ​(d) between 139 and 158​, inclusive are on time.
A certain flight arrives on time 81 percent of the time. Suppose 113 flights are randomly...
A certain flight arrives on time 81 percent of the time. Suppose 113 flights are randomly selected. Use the normal approximation to the binomial to approximate the probability that ​(a) exactly 89 flights are on time. ​(b) at least 89 flights are on time. ​(c) fewer than 87 flights are on time. ​(d) between 87 and 97 ​, inclusive are on time.
A certain flight arrives on time 89 percent of the time. Suppose 118 flights are randomly...
A certain flight arrives on time 89 percent of the time. Suppose 118 flights are randomly selected. Use the normal approximation to the binomial to approximate the probability that ​ (a) exactly 95 flights are on time.​ (b) at least 95 flights are on time.​ c) fewer than 107 flights are on time. ​(d) between 107 and 108​, inclusive are on time.
A certain flight arrives on time 90 percent of the time. Suppose 190 flights are randomly...
A certain flight arrives on time 90 percent of the time. Suppose 190 flights are randomly selected. Use the normal approximation to the binomial to approximate the probability that ​(a) exactly 163 flights are on time. ​(b) at least 163 flights are on time. ​(c) fewer than 182 flights are on time. ​(d) between 182 and 183​, inclusive are on time.