Recitation 9 (Sampling Distribution).docx - STAT 1450 Recitation Activity 9 Sampling Distributions General Rules of Probability Name Austin Gruber TA

Recitation 9 (Sampling Distribution).docx - STAT 1450...

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STAT 1450 Recitation Activity 9 Name: Austin Gruber Sampling Distributions & General Rules of Probability TA: Eunseop Kim Date: 10/16/18 OBJECTIVES Students will compute probabilities based upon the Central Limit Theorem. Students will use a Statistical Applet to simulate a random phenomenon. Students will explore the asymptotic behavior of sample means from various distributions. Part I – Sampling Distributions & The Central Limit Theorem 1. Statistics from Cornell’s Northeast Regional Climate Center indicate that Ithaca, NY, gets an average of 35.4” of rain each year, with a standard deviation of 4.2”. Assume that a Normal model applies. (Problem from Intro Stats by De Veaux, Velleman, Bock – 3 rd Edition) a) During what percentage of years does Ithaca get more than 40” of rain? P(x> 40) = P( 40 – 35.4)/4.2 = P( z > 1.10) = P(z < 1.10) = 0.8643 = P(z > 1.10)= 1.00 – 0.8643 = 0.1357 or 13.57% b) Less than how much rain falls in the driest 20% of all years? (20% z-score) = -2.05 -2.05 = (x – 35.4)/ 4.2 -8.61 = x – 35.4 X= 26.79” c) A Cornell University student is in Ithaca for 4 years. Let ´ y represent the mean amount of rain for those 4 years. Describe the sampling distribution model of this sample mean, ´ y .
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