EX 8 - STAT 400 1 Examples for Spring 2011 At Initech the...

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STAT 400 Examples for 03/02/2011 Spring 2011 1. At Initech , the salaries of the employees are normally distributed with mean μ = $36,000 and standard deviation σ = $5,000. a) Mr. Smith is paid $42,000. What proportion of the employees of Initech are paid less that Mr. Smith? P ( X < 42,000 ) = - < 000 , 5 000 , 36 000 , 42 Z P = P ( Z < 1.20 ) = 0.8849 . b) What proportion of the employees have their salaries over $40,000? P ( X > 40,000 ) = - > 000 , 5 000 , 36 000 , 40 Z P = P ( Z > 0.80 ) = 1 – 0.7881 = 0.2119 . c) Suppose 10 Initech employees are randomly and independently selected. What is the probability that 3 of them have their salaries over $40,000? Let Y = number of employees (out of 10) who have salaries over $40,000. Then Y has Binomial distribution, n = 10, p = 0.2119 ( see (b) ). P ( Y = 3 ) = ( ) ( ) 7 3 7881 . 0 2119 . 0 3 10 C = 0.2156 . d) What proportion of the employees have their salaries between $30,000 and $40,000? P
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EX 8 - STAT 400 1 Examples for Spring 2011 At Initech the...

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