Question

(Can this be done on a Ti-84?) A certain flight arrives on time 83 percent of...

(Can this be done on a Ti-84?) A certain flight arrives on time 83 percent of the time. Suppose140 flights are randomly selected. Use the normal approximation to the binomial to approximate the probability that

?(a) exactly 109 flights are on time.

?(b) at least 109 flights are on time.

?(c) fewer than 114 flights are on time.

?(d) between 114 and 128 inclusive are on time.

Homework Answers

Answer #1

Solution:-

p = 0.83

n = 140

Mean = n × p

Mean = 140 × 0.83

Mean = 116.2

a) The probability that exactly 109 flights are on time is 0.021.

x = 109

By applying normal distruibution:-

z = - 1.162

P(z = - 1.162) = 0.021

b) The probability that at least 109 flights are on time is 0.8776.

x = 109

By applying normal distruibution:-

z = - 1.162

P(z > -1.162) = 0.8776

c) The probability that a fewer than 114 flights are on time is 0.3101.

x = 114

By applying normal distruibution:-

z = - 0.495

P(z < - 0.495) = 0.3101

d) The probability that between 114 and 128 inclusive are on time is 0.6857.

x1 = 114

x2 = 128

By applying normal distruibution:-

z1 = - 0.495

z2 = 2.65

P(- 0.495 < z < 2.65) = P(z > - 0.495) - P(z > 2.65)

P(- 0.495 < z < 2.65) = 0.6897 - 0.004

P(- 0.495 < z < 2.65) = 0.6857

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 an? airline, flights on a certain route are on time 75?%of the time. Suppose...
According to an? airline, flights on a certain route are on time 75?%of the time. Suppose 24 flights are randomly selected and the number of? on-time flights is recorded. ?(a) Explain why this is a binomial experiment. ?(b) Find and interpret the probability that exactly 14 flights are on time. ?(c) Find and interpret the probability that fewer than 14 flights are on time. ?(d) Find and interpret the probability that at least 14 flights are on time. ?(e) Find...
In studies for a​ medication, 4 percent of patients gained weight as a side effect. Suppose...
In studies for a​ medication, 4 percent of patients gained weight as a side effect. Suppose 416 patients are randomly selected. Use the normal approximation to the binomial to approximate the probability that ​(a) exactly 6 patients will gain weight as a side effect. ​(b) 6 or fewer patients will gain weight as a side effect. ​(c) 27 or more patients will gain weight as a side effect. ​(d) between 6 and 14​, ​inclusive, will gain weight as a side...
Suppose that it is believed that 20 percent of people in a certain region of South...
Suppose that it is believed that 20 percent of people in a certain region of South Carolina will become infected by the COVID-19 virus. Consider a random sample of 200 people taken from this region. What is the probability that, of these 200 people, more than 25 but fewer than 45 of the people will become infected with the virus? Use the normal approximation to the binomial to determine this probability. Verify that the sample size is large enough for...
Census data show that 3?% of students in a certain country went to college or a...
Census data show that 3?% of students in a certain country went to college or a trade school within a year of graduating from high school. A random sample of 453 high school graduates is selected. Use the normal approximation to the binomial distribution to complete parts a through e below. a. What are the mean and standard deviation of this? distribution? b. What is the probability that 16 or fewer students will go to? college? c. What is the...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT