Questions: (a) Explain why this is a binomial experiment. (b) Determine the values of n and p (c) Find and interpret the probability that exactly 16 flights are on time. (d) Find and interpret the probability that fewer than 16 flights are on time. (e) Find and interpret the probability that at least 16 flights are on time. (C) Find and interpret the probability that between 14 and 16 flights, inclusive, are on time. (Round to the nearest whole number as needed) (Round to four decimal places as needed) In 100 trials of this experiment, it is expected that about will result in fewer than 16 flights being on time. (Round to the nearest whole number as needed) (e) Using the binomial distribution the probability that at least 16 flights are on time is (Round to four decimal places as needed) In 100 trials of this experiment, it is expected that about will result in at least 16 flights being on time. (Round to the nearest whole number as needed) 7. (Round to four decimal places as needed) In 100 trials of this experiment, it is expected that about will result in between 14 and 18 flights, inclusive, being on time. (Round to the nearest whole number as needed)

(a) Explain why this is a binomial experiment. (b) Determine the values of n and p (c) Find and interpret the probability that exactly 16 flights are on time. (d) Find and interpret the probability that fewer than 16 flights are on time. (e) Find and interpret the probability that at least 16 flights are on time. (C) Find and interpret the probability that between 14 and 16 flights, inclusive, are on time. (Round to the nearest whole number as needed) (Round to four decimal places as needed) In 100 trials of this experiment, it is expected that about will result in fewer than 16 flights being on time. (Round to the nearest whole number as needed) (e) Using the binomial distribution the probability that at least 16 flights are on time is (Round to four decimal places as needed) In 100 trials of this experiment, it is expected that about will result in at least 16 flights being on time. (Round to the nearest whole number as needed) 7. (Round to four decimal places as needed) In 100 trials of this experiment, it is expected that about will result in between 14 and 18 flights, inclusive, being on time. (Round to the nearest whole number as needed)
Transcript text: (a) Explain why this is a binomial experiment. (b) Determine the values of $n$ and $p$ (c) Find and interpret the probability that exactly 16 flights are on time. (d) Find and interpret the probability that fewer than 16 flights are on time. (e) Find and interpret the probability that at least 16 flights are on time. (C) Find and interpret the probability that between 14 and 16 flights, inclusive, are on time. (Round to the nearest whole number as needed) (Round to four decimal places as needed) In 100 trials of this experiment, it is expected that about $\square$ will result in fewer than 16 flights being on time. (Round to the nearest whole number as needed) (e) Using the binomial distribution the probability that at least 16 flights are on time is $\square$ $\square$ (Round to four decimal places as needed) In 100 trials of this experiment, it is expected that about $\square$ $\square$ will result in at least 16 flights being on time. (Round to the nearest whole number as needed) $\square$ 7. (Round to four decimal places as needed) In 100 trials of this experiment, it is expected that about $\square$ $\square$ will result in between 14 and 18 flights, inclusive, being on time. (Round to the nearest whole number as needed)
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Solution

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Solution Steps

Step 1: Explanation of the Binomial Experiment

This scenario represents a binomial experiment because it satisfies the following criteria:

  • There is a fixed number of trials, \( n = 20 \) (the number of flights).
  • Each trial has two possible outcomes: a flight is either on time (success) or not on time (failure).
  • The probability of success, \( p = 0.8 \), remains constant for each trial.
  • The trials are independent; the outcome of one flight does not affect the others.
Step 2: Values of \( n \) and \( p \)

The values determined for the binomial experiment are:

  • Number of trials: \( n = 20 \)
  • Probability of success: \( p = 0.8 \)
Step 3: Probability of Exactly 16 Flights Being On Time

To find the probability that exactly 16 flights are on time, we use the binomial probability formula:

\[ P(X = x) = \binom{n}{x} \cdot p^x \cdot q^{n-x} \]

Substituting the values:

\[ P(X = 16) = \binom{20}{16} \cdot (0.8)^{16} \cdot (0.2)^{4} = 0.2182 \]

Thus, the probability that exactly 16 flights are on time is \( 0.2182 \).

Final Answer

The values of \( n \) and \( p \) are \( n = 20 \) and \( p = 0.8 \). The probability that exactly 16 flights are on time is \( 0.2182 \).

\[ \boxed{n = 20, \, p = 0.8, \, P(X = 16) = 0.2182} \]

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