**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.

Answered: Image /qna-images/answer/7d5f7a15-6593-48bf-9c39-610ba4d060a4.jpg

Answered: NBC News reported on May 2, 2013, that…

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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Solve a,b,c. Typed answer please. I will rate
Many track hurdlers believe that they have a better chance of winning if they start in the inside lane that is closest to the field. For the data below, the lane closest to the field is Lane 1, the next lane is Lane 2, and so on until the outermost lane, Lane 6. The data lists the number of wins for track hurdlers in the different starting positions. Calculate the chi-square test statistic x to test the claim that the probabilities of winning are the same in the different positions. Use α = 0.05. The results are based on 240 wins. Starting Position 3 4 5 6 1 2 Number of Wins 44 32 33 50 36 45 O A. 6.750 O B. 12.592 O C. 15.541 O D. 9.326 C
If A and Bare events with P(A) 0.6, P(A OR B) 0.98, P(A AND B) 0.02, find F(B). Provide your answer below: .4 9 FEEDBACK
The probabilities of all the values of a random variableX must: OA. average to a small and negative number. OB. add up to 1. OC. average to 0. D. none of the above,
(iii) Find (or estimate) the P-value. OP-value > 0.250 O 0.125 < P-value < 0.250 O 0.050 < P-value < 0.125 O 0.025 < P-value < 0.050 O 0.005< P-value < 0.025 OP-value < 0.005 Sketch the sampling distribution and show the area corresponding to the P-value. O -4 -2 0 2 2 M 2 DO Q -2 -2 (iv) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a? O At the a= 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. O At the a= 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. O At the a= 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant. O At the a= 0.01 level, we reject the null hypothesis and conclude the data are statistically significant. (v) Interpret your conclusion in the context of the application. O Fail to reject the null hypothesis, there…
Consider X is a random variable and has equal probability of being -1,0,+1. What is the correlation between X and Y while Y=X*X.
For each probability and percentile problem, draw the picture.A random number generator picks a number from 1 to 8 in a uniform manner. Part (e) ? = rounded to two decimal places) Part (f) P(3.5 < X < 7.25) = (Enter an exact number as an integer, fraction, or decimal.) Part (g) P(X > 3.67) = (rounded to two decimal places)
Let X be a B (10, 1/2) random variable. What is the probability that X = 5?
Q2: A random variable X has a mean = 8, a variance o² = 9, and an unknown probability distribution. Find P(X-826).
A random sample of n1 = 10 regions in New England gave the following violent crime rates (per million population). x1: New England Crime Rate 3.3 3.7 4.2 3.9 3.3 4.1 1.8 4.8 2.9 3.1 Another random sample of n2 = 12 regions in the Rocky Mountain states gave the following violent crime rates (per million population). x2: Rocky Mountain Crime Rate 3.9 4.1 4.5 5.5 3.3 4.8 3.5 2.4 3.1 3.5 5.2 2.8 Assume that the crime rate distribution is approximately normal in both regions. Do the data indicate that the violent crime rate in the Rocky Mountain region is higher than in New England? Use ? = 0.01. Solve the problem using both the traditional method and the P-value method. (Test the difference ?1 − ?2. Round the test statistic and critical value to three decimal places.) test statistic critical value
Toss five fair coins and let x equal the number of heads observed. a. Identify the sample points associated with this experiment, and assign a value of x to each sample point. Then list all the possible values of x. b. Calculate p(x) for the values x = 1 and x = 2. c. Construct a probability histogram for p(x). d. What is P(x = 1 or x = 4)?
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