Question

The Normal Approximation to the Binomial Distribution Consider the probability that less than 14 out of 157 flights will be delayed. Assume the probability that a given flight will be delayed is 12%. Approximate the probability using the normal distribution. Round your answer to three decimal places. 1. First show that the normal approximation to the binomial can be used meaning show that np\geq 10 and n(1-p)\geq 10 2. The parameters needed for the normal distribution \(\mu\) and \(\sigma\). Find them by using \(\mu = np\) and \(\sigma = \sqrt{np(1 - p)}\). Round to two or three decimal places: 3. To Find p(x < 14), the probability than less than 14 out of 157 flights will be delayed by using the normal approximation, you have to apply the continuity correction first. Rewrite p(x < 14) with the continuity correction applied. Hint: the value 14 is not included. I 4. Using the value you found in question 3, and \(\mu\) and \(\sigma\) you found in question 2, find the probability that less than 14 out of 157 flights will be delayed by using the normal distribution. Include a sketch of the normal distribution and shade the area that represents the probability. Round to three decimal places.

          The Normal Approximation to the Binomial Distribution
Consider the probability that less than 14 out of 157 flights will be delayed. Assume the
probability that a given flight will be delayed is 12%. Approximate the probability using the
normal distribution. Round your answer to three decimal places.
1. First show that the normal approximation to the binomial can be used meaning show that
np\geq 10 and n(1-p)\geq 10
2. The parameters needed for the normal distribution \(\mu\) and \(\sigma\). Find them by using \(\mu = np\) and
\(\sigma = \sqrt{np(1 - p)}\). Round to two or three decimal places:
3. To Find p(x < 14), the probability than less than 14 out of 157 flights will be delayed by using
the normal approximation, you have to apply the continuity correction first. Rewrite p(x < 14)
with the continuity correction applied. Hint: the value 14 is not included.
I
4. Using the value you found in question 3, and \(\mu\) and \(\sigma\) you found in question 2, find the
probability that less than 14 out of 157 flights will be delayed by using the normal distribution.
Include a sketch of the normal distribution and shade the area that represents the probability.
Round to three decimal places.

The Normal Approximation to the Binomial Distribution
Consider the probability that less than 14 out of 157 flights will be delayed. Assume the
probability that a given flight will be delayed is 12%. Approximate the probability using the
normal distribution. Round your answer to three decimal places.
1. First show that the normal approximation to the binomial can be used meaning show that
np≥10 and n(1-p)≥10
2. The parameters needed for the normal distribution μ and σ. Find them by using μ = np and
σ = √(np(1 - p)). Round to two or three decimal places:
3. To Find p(x < 14), the probability than less than 14 out of 157 flights will be delayed by using
the normal approximation, you have to apply the continuity correction first. Rewrite p(x < 14)
with the continuity correction applied. Hint: the value 14 is not included.
I
4. Using the value you found in question 3, and μ and σ you found in question 2, find the
probability that less than 14 out of 157 flights will be delayed by using the normal distribution.
Include a sketch of the normal distribution and shade the area that represents the probability.
Round to three decimal places.

Added by Virginia B.

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