Lesson 26 Assignment key - Copy

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Pennsylvania State University *

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120N

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Statistics

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May 1, 2024

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pdf

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Uploaded by CoachProtonSardine33 on coursehero.com

Lesson 26: Combining and Transforming Random Variables Name: Period: 1. The distribution for the random variable G has a mean of 12 and a standard deviation of 5. The distribution of the random variable S has a mean of 9 and a standard deviation of 4. If G and S are independent, what are the mean and standard deviation of G-S. 2. On a roulette wheel, there are 38 slots numbers 1-36 along with 0 and 00. Half of the 36 slots are red and the other half are black. 0 and 00 are green slots. Let’s say that we walk up to a roulette wheel and place a $5 bet on black. If the ball lands on a black slot we get our original bet back ($5) plus another $5 for winning. Of course, if the ball lands on a red or green slot we lose our $5 bet. What will be our expected gain and standard deviation if we play two games betting $5 each time on black? Term Definition (your own words) Examples Independent Random Variable StatsWithHogan©2019 Lesson 26 Assignment-1 Mo s No Ms To.s VJo2tJ2 Mo s 12 9 Jo s V 52 42 Mo s 3 Jo s ITT 6.40 f 1st game f 2ndgamefxzofso.is zoomfF fg5I YgDzY9g the 512 1 54 8 Tx 5.00 the 0.2631 µ y µ t µ y E I E3 tz ou.IS

3. The random variable Z has a mean of 15 and a standard deviation of 6. The random variable will be defined as J=10 + 3Z. What are the mean and standard deviation of J? 4 . Universities and colleges use ACT scores as part of the admissions process. Here is last year’s national data for ACT scores. ACT Math score μ x = 20.9 σ x = 4.1 ACT Reading score μ y = 21.3 σ y = 4.4 What are the mean and standard deviation of the total score X + Y for a randomly selected applicant to a college or university? StatsWithHogan©2019 Lesson 26 Assignment-2 If 101 3 Uz f 3 Tz 101 3115 f 316 µ 55 Tj 18 Math Score ACT 4 Reading Score ACT µ xty Uxt µ y Txty VJ 2tJy2 20.91 21.3 V 4 1 2 4.47 µ xty 42.2 T y 6.01

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