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# 6.3.q1 - Student Grady Simonton Course Mathll9 Elementary...

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Unformatted text preview: Student: Grady Simonton Course: Mathll9: Elementary Statistics - Spring 2010 - CRN: 49239 Instructor: Shawn Parvini - 16 weeks Date: 3/18/10 Book: Triola: Elementary Statistics, lle Time: 4:05 PM Find the area of the shaded region. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15. 130 While either technology or the standard normal distribution table can be used to ﬁnd the area, for the purposes of this problem, use the standard normal distribution table. To ﬁnd an area with a nonstandard normal distribution, ﬁrst convert the normal random variable, x, to the standard normal random variable, 2, using the formula below, where p is the mean and o is the standard deviation. X — 1-1 z = o 130 - 100 _ = Substrtute. 15 = 2.00 Simplify. Therefore, the z score corresponding to x = 130 is z = 2.00. The shaded region shown in the problem statement has the same area as the shaded region shown to the right. The shaded region in the graph to the right is the area to the left of 2.00 in a standard normal distribution with a mean of 0 and a standard deviation of l. Find the area to the left of the z score in the standard normal distribution table. Begin with the z score of 2.0 by locating 2.0 in the leﬁ column; next ﬁnd the value in the adjoining row of probabilities that is directly below 0.00. Use the standard normal distribution table to ﬁnd the area to the left of z = 2.00. The area of to the left of z = 2.00 is 0.9772. Therefore, the area of the shaded region is 0.9722. Page 1 ...
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