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NBC News reported on May 2, 2013, that 1 in 20 children in the United States have a food allergy of some sort. Consider selecting a random sample of 15 children and let X be the number in the sample who have a food allergy. Then X- Bin(15, 0.05). (Round your probabilities to three decimal places.) n USE SALT (a) Determine both P(X s 2) and P(X < 2). P(X s 2) = P(X < 2) = (b) Determine P(X 2 3). P(X 2 3) = (c) Determine P(1 sX< 2). P(1 sxs 2) =

NBC News reported on May 2, 2013, that 1 in 20 children in the United States have a food allergy of some sort. Consider selecting a random sample of 15 children and let X be the number in the sample who have a food allergy. Then X- Bin(15, 0.05). (Round your probabilities to three decimal places.) n USE SALT (a) Determine both P(X s 2) and P(X < 2). P(X s 2) = P(X < 2) = (b) Determine P(X 2 3). P(X 2 3) = (c) Determine P(1 sX< 2). P(1 sxs 2) =

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Educational Website Content: Binomial Distribution and Food Allergies** --- NBC News reported on May 2, 2013, that 1 in 20 children in the United States have a food allergy of some sort. Consider selecting a random sample of 15 children and let \( X \) be the number in the sample who have a food allergy. Then \( X \sim \text{Binomial}(15, 0.05) \). (Round your probabilities to three decimal places.) ### Tasks **(a)** Determine both \( P(X \leq 2) \) and \( P(X < 2) \). - \( P(X \leq 2) = \underline{\hspace{2cm}} \) - \( P(X < 2) = \underline{\hspace{2cm}} \) **(b)** Determine \( P(X \geq 3) \). - \( P(X \geq 3) = \underline{\hspace{2cm}} \) **(c)** Determine \( P(1 \leq X \leq 2) \). - \( P(1 \leq X \leq 2) = \underline{\hspace{2cm}} \) **(d)** What are \( E(X) \) and \( \sigma_X^2 \)? (Round your answers to two decimal places.) - \( E(X) = \underline{\hspace{2cm}} \) - \( \sigma_X = \underline{\hspace{2cm}} \) **(e)** In a sample of 30 children, what is the probability that none has a food allergy? --- The use of the binomial distribution allows us to calculate the probabilities of different outcomes related to food allergies in children, utilizing real-world data for a practical understanding of statistical concepts.
Transcribed Image Text:**Educational Website Content: Binomial Distribution and Food Allergies** --- NBC News reported on May 2, 2013, that 1 in 20 children in the United States have a food allergy of some sort. Consider selecting a random sample of 15 children and let \( X \) be the number in the sample who have a food allergy. Then \( X \sim \text{Binomial}(15, 0.05) \). (Round your probabilities to three decimal places.) ### Tasks **(a)** Determine both \( P(X \leq 2) \) and \( P(X < 2) \). - \( P(X \leq 2) = \underline{\hspace{2cm}} \) - \( P(X < 2) = \underline{\hspace{2cm}} \) **(b)** Determine \( P(X \geq 3) \). - \( P(X \geq 3) = \underline{\hspace{2cm}} \) **(c)** Determine \( P(1 \leq X \leq 2) \). - \( P(1 \leq X \leq 2) = \underline{\hspace{2cm}} \) **(d)** What are \( E(X) \) and \( \sigma_X^2 \)? (Round your answers to two decimal places.) - \( E(X) = \underline{\hspace{2cm}} \) - \( \sigma_X = \underline{\hspace{2cm}} \) **(e)** In a sample of 30 children, what is the probability that none has a food allergy? --- The use of the binomial distribution allows us to calculate the probabilities of different outcomes related to food allergies in children, utilizing real-world data for a practical understanding of statistical concepts.
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