A pathological video game user (PVGU) is a video game user that averages 31 or more hours a week of gameplay. According to the article “Pathological Video Game Use among Youths: A Two-Year Longitudinal Study” (Pediatrics, Vol. 127, No. 2, pp. 319–329) by D. Gentile et al., in 2011, about 9% of children in grades 3–8 were PVGUs. Suppose that, today, five youths in grades 3–8 are randomly selected. Let X represent the number of youths who are PVGUs.n = p = 1 – p = Prepare the probability distribution for the random variable X. Complete the following table. Round your answers to 4 decimal places e.g. 0.XXXX or .XXXX.X = xP(X=x)0 1 2 3 4 5 ∑=1.0000∑=1.0000 Calculate the probability that EXACTLY three youths are PVGUs. Round your answers to 4 decimal places e.g. 0.XXXX or .XXXX.P(X = 3) = Calculate the probability that AT LEAST two youths are PVGUs. Round your answers to 4 decimal places e.g. 0.XXXX or .XXXX.P(X ≥ 2) = Calculate the probability that AT MOST three youths are PVGUs. Round your answers to 4 decimal places e.g. 0.XXXX or .XXXX.P(X ≤ 3) = Calculate the probability that BETWEEN two and four youths are PVGUs. Round your answers to 4 decimal places e.g. 0.XXXX or .XXXX.P(2 < X < 4) = Calculate the probability that BETWEEN two and four (INCLUSIVE) youths are PVGUs. Round your answers to 4 decimal places e.g. 0.XXXX or .XXXX.P(2 ≤ X ≤ 4) = Calculate the mean of the random variable X. Round your answers to 4 decimal places e.g. 0.XXXX or .XXXX.E(X) = µ = Calculate the variance of the random variable X. Round your answers to 4 decimal places e.g. 0.XXXX or .XXXX.σ2 = Calculate the standard deviation of the random variable X. Round your answers to 4 decimal places e.g. 0.XXXX or .XXXX.σ =

Here use binomial theorem P = 0.09 q = 0.91 n = 5

Answered: A pathological video game user (PVGU)…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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A pathological video game user (PVGU) is a video game user that averages 31 or more hours a week of gameplay. According to the article “Pathological Video Game Use among Youths: A Two-Year Longitudinal Study” (Pediatrics, Vol. 127, No. 2, pp. 319–329) by D. Gentile et al., in 2011, about 9% of children in grades 3–8 were PVGUs. Suppose that, today, five youths in grades 3–8 are randomly selected. Let X represent the number of youths who are PVGUs.

n =
p =
1 – p =
Prepare the probability distribution for the random variable X. Complete the following table. Round your answers to 4 decimal places e.g. 0.XXXX or .XXXX.

X = x P(X=x)

0

1

2

3

4

5

∑=1.0000∑=1.0000
Calculate the probability that EXACTLY three youths are PVGUs. Round your answers to 4 decimal places e.g. 0.XXXX or .XXXX.

P(X = 3) =

Calculate the probability that AT LEAST two youths are PVGUs. Round your answers to 4 decimal places e.g. 0.XXXX or .XXXX.

P(X ≥ 2) =

Calculate the probability that AT MOST three youths are PVGUs. Round your answers to 4 decimal places e.g. 0.XXXX or .XXXX.

P(X ≤ 3) =

Calculate the probability that BETWEEN two and four youths are PVGUs. Round your answers to 4 decimal places e.g. 0.XXXX or .XXXX.

P(2 < X < 4) =

Calculate the probability that BETWEEN two and four (INCLUSIVE) youths are PVGUs. Round your answers to 4 decimal places e.g. 0.XXXX or .XXXX.

P(2 ≤ X ≤ 4) =

Calculate the mean of the random variable X. Round your answers to 4 decimal places e.g. 0.XXXX or .XXXX.

E(X) = µ =

Calculate the variance of the random variable X. Round your answers to 4 decimal places e.g. 0.XXXX or .XXXX.

σ² =

Calculate the standard deviation of the random variable X. Round your answers to 4 decimal places e.g. 0.XXXX or .XXXX.

σ =

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X = x	P(X=x)
0
1
2
3
4
5
	∑=1.0000∑=1.0000