Solution Found!
On-Time Flights According to American Airlines, Flight 215
Chapter 7, Problem 21AYU(choose chapter or problem)
Problem 21AYU
On-Time Flights According to American Airlines, Flight 215 from Orlando to Los Angeles is on time 90% of the time. Randomly select 150 flights and use the normal approximation to the binomial to
(a) approximate the probability that exactly 130 flights are on time.
(b) approximate the probability that at least 130 flights are on time.
(c) approximate the probability that fewer than 125 flights are on time.
(d) approximate the probability that between 125 and 135 flights, inclusive, are on time.
Questions & Answers
QUESTION:
Problem 21AYU
On-Time Flights According to American Airlines, Flight 215 from Orlando to Los Angeles is on time 90% of the time. Randomly select 150 flights and use the normal approximation to the binomial to
(a) approximate the probability that exactly 130 flights are on time.
(b) approximate the probability that at least 130 flights are on time.
(c) approximate the probability that fewer than 125 flights are on time.
(d) approximate the probability that between 125 and 135 flights, inclusive, are on time.
ANSWER:
Answer:
Step 1 of 4
Given, On-Time Flights According to American Airlines, Flight 215 from Orlando to Los Angeles is on time 90% of the time. Randomly select 150 flights and use the normal approximation to the binomial to
(a) Given, , q = 1 - p = 0.1 and n = 150
We know that
And
Now,
We know that exact probability P(X = )
Approximate Probability Using Normal Curve P(
Here, P(X = 130)
Approximate Probability Using Normal Curve P(
P(129.5 < X < 130.5) = P(
P(-1.5 < Z < -1.23)
P(Z < -1.22) = 0.1112 (Area under Normal curve table)
P(Z > -1.49) = 0.0681 (Area under Normal curve table)
Now, P(Z < -1.22) - P(Z > -1.49) = 0.0431
Therefore, P(X = 130) = 0.0431