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QUIZ+4+SOLUTIONS

# QUIZ+4+SOLUTIONS - c What IQ score will place an...

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QUIZ #4 MATH 1070 Spring 2008 March 19 th , 2008 1. [4 points] The length of human pregnancies from conception to birth varies according to a distribution that is approximately normal with a mean of 266 days and standard deviation of 16 days. a. Find the probability that the length of pregnancies falls between 234 and 272 days P ( 29 272 234 X = Standardize =P - - 16 266 272 16 266 234 Z =P ( 29 38 . 0 2 - Z = 0.06253 2 nd VARS => NormCDF(-2,0.38)=0.6253 b. What must a woman’s length of pregnancy be to be classified in the longest 2.5% of all human pregnancies? Therefore, P ( 29 298 X =0.025

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QUIZ #4 MATH 1070 Spring 2008 March 19 th , 2008 2. [4 points] In a large population of adults, the mean IQ is 100 with a standard deviation of 20. Given that the IQ scores are normally distributed a. Find the probability that an individual has an IQ less than 100 P ( 29 100 X =0.5 b. Find the probability that an individual has an IQ between 80 and 120 P ( 29 120 80 X =68%=0.68 by the empirical rule.
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Unformatted text preview: c. What IQ score will place an individual’s IQ in the top 1%? With a proportion of 1% on the right, we have 99% on the left. The Z table can only be read from LEFT TO RIGHT. So we have to find the Z value that yields a proportion of 99%=0.99. Using the Z table, this Z=2.33. Now going by the formula X=Zσ+µ X=2.33*20+100=146.6. One has to score at least 146.6 in the IQ test to be placed in the top 1% of all IQ test takers! QUIZ #4 MATH 1070 Spring 2008 March 19 th , 2008 3. Given the following diagram and that X is a random variable a. Find the probability P ) 2 4 . ( ≤ ≤ X A= h b * * 2 1 = 8 . * ) 4 . 2 ( * 2 1-= 64 . 8 . * 8 . 8 . * ) 6 . 1 ( * 2 1 = = b. Classify X as a either continuous or discrete random variable. Explain your reasoning This is a continuous random variable because X can attain infinite values over the interval ) 2 4 . ( ≤ ≤ X...
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