Answers_to_ADDITIONAL_PROBLEMS_-_Section_1.3

Answers_to_ADDITIONAL_PROBLEMS_-_Section_1.3 - P(X< x =...

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ADDITIONAL PROBLEMS – SECTION 1.3 Checking account balances are ~ N(1325, 25). Bill has a balance of $1270. a) What is the probability an account will have less money than Bill’s? P(X < 1270) = P(Z < 25 1325 1270 ) = P(Z < -2.2) = 0.0139 b) What is the probability an account balance will be more than $1380? P(X > 1380) = P(Z > 25 1325 1380 ) = P(Z > 2.2) = 1 – P(Z < 2.2) = 1 - .9861 = 0.0139 c) What is the probability an account balance will be exactly $1380? P(X = 1380) = 0 d) What is the probability an account will have less than $1325 (the mean)? P(X < 1325) = 0.5 e) What is the probability that an account will have between $1310 and $1390? P(1310 < X < 1390) = P( 25 1325 1310 < Z < 25 1325 1390 ) = P(-0.6 < Z < 2.6) = P(Z < 2.6) – P(Z < -0.6) = 0.9953 – 0.2743 = 0.7210 f) What is the probability an account will have less than $10? P(X < 10) = P(Z < 25 1325 10 ) = P(Z < -52.6) = 0 g) What is the account balance, x 0 , such that the percentage of balances less than it is 23%?
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Unformatted text preview: P(X < x ) = 0.23 P(Z < z ) = 0.23 z = -0.74 z = x -0.74 = 25 1325 x x =1306.50 h) What is the account balance, x , such that the probability of a balance being more than it is 0.15? P(X > x ) = 0.15 P(Z > z ) = 0.15 1- P(Z < z ) = 0.15 P(Z < z ) = 0.85 z = 1.04 z = x 1.04 = 25 1325 x x =1351 i) What is the account balance, x , such that the probability of a balance being more than it is 0.5? (Hint: you should be able to do this one without math.) 1325 (the mean) j) Between what 2 central values do 40% of the balances fall? P(x 1 < X < x 2 ) = 0.40 P(-z < Z < z ) = 0.40 2P(Z < z ) - 1 =0.40 P(Z < z ) = 0.70 z = 0.525 z = x Two answers, one for the negative z and one for the positive z. 0.525 = 25 1325 2 x x 2 = 1338.10 -0.525 = 25 1325 1 x x 1 = 1311.90...
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This note was uploaded on 02/28/2012 for the course STAT 301 taught by Professor Staff during the Spring '08 term at Purdue.

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