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Unformatted text preview: outside this range are unusable. One machine shop sells washers at $3.00 per 1000. Their thicknesses are normally distributed with a mean of 0.1200 inch and a standard deviation of 0.0010 inch. Another machine shop sells washers at $2.60 per 1000. Their thicknesses are normally distributed with a mean of .1200 inch and a standard deviation of .0015 inch. Which shop offers a better deal? 4. Jim takes two papers X and Y in an examination. His score on X has a N (54,36) distribution and his score on Y has a N (66 , 64) distribution. He will pass the examination if his total score is 100 or above. What is his probability of passing the examination? Assume X and Y are independent. 5. Prove the following results: a. If ² ~ ¶· ( ¸ , ¹ ) , then º² ~ ¶· ( ¸ , ¹ º ) for any º > 0 . b. If ² ~ ¶· ( » , 2 ) and ¼ ~ µ½¾ ( ¿ ) , then µ ² > ¿ 2 À = µ ( ¼ < » ) ....
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