Math Problem Statement

According to​ flightstats.com, American Airlines flights from Dallas to Chicago are on time

8080​%

of the time. Suppose

2525

flights are randomly​ selected, and the number of​ on-time flights is recorded. Using the binomial​ distribution, determine the values of n and p.

nequals=2525

​(Type an integer or a decimal. Do not​ round.)

Part 3

pequals=. 80.80

​(Type an integer or a decimal. Do not​ round.)

Part 4

​(c) Using the binomial​ distribution, the probability that exactly

1717

flights are on time is

. 0623.0623.

​(Round to four decimal places as​ needed.)

Part 5

Interpret the probability.

In 100 trials of this​ experiment, it is expected that about

66

will result in exactly

1717

flights being on time.

​(Round to the nearest whole number as​ needed.)

Part 6

​(d) Using the binomial​ distribution, the probability that fewer than

1717

flights are on time is

. 0468.0468.

​(Round to four decimal places as​ needed.)

Part 7

Interpret the probability.

In 100 trials of this​ experiment, it is expected that about

55

will result in fewer than

1717

flights being on time.

​(Round to the nearest whole number as​ needed.)

Part 8

​(e) Using the binomial​ distribution, the probability that at least

1717

flights are on time is

. 9532.9532.

​(Round to four decimal places as​ needed.)

Part 9

Interpret the probability.

In 100 trials of this​ experiment, it is expected that about

9595

will result in at least

1717

flights being on time.

​(Round to the nearest whole number as​ needed.)

Part 10

​(f) Using the binomial​ distribution, the probability that between

1515

and

1717

​flights, inclusive, are on time is

enter your response here.

​(Round to four decimal places as​ needed.)

Solution

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Math Problem Analysis

Mathematical Concepts

Probability
Binomial Distribution

Formulas

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)
P(a ≤ X ≤ b) = sum of binomial probabilities for each k between a and b

Theorems

Binomial Theorem

Suitable Grade Level

Grades 11-12