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Quiz 2 foe Statistics spring 2017 (2) [Compatibility Mode-Microsoft word ES MAIL

ID: 3334689 • Letter: Q

Question

Quiz 2 foe Statistics spring 2017 (2) [Compatibility Mode-Microsoft word ES MAILINGS REVIEW VIEW For borrowers with good credit scores, the mean debt for revolving and installment accounts is $15,015. Assume the standard deviation is $3540 and debt amounts are normally distributed. 1. What's the probability that the debt for a borrower with good credit is more than $18,000? a. What's the probability that the debt for a borrower with good credit is between S17,000 and $19,000? b. c. What are the cut offs of the middle 36%?

Explanation / Answer

Mean = 15015, std. dev. = 3540

Formula: Z = (X-mean)/std.dev.

a) P(X > 18000) = 1 - P(X < 18000) = 1 - P(Z < (18000 - 15015)/3540) = 1 - P(Z < 0.8432) = 1 - 0.8004 = 0.1996

b) P(17000 < X < 19000) = P(X < 19000) - P(X < 17000)
= P(Z < (19000 - 15015)/3540) - P(Z < (17000-15054)/3540) = P(Z < 1.1257) - P(Z < 0.5497)
= 0.8699 - 0.7087 = 0.1612

c) P(x1 < X < x2) = 0.36
P(Z < (x2 - 15015)/3540) - P(Z < (x1 - 15015)/3540) = 0.36
P(Z < (x2 - 15015)/3540) = 0.68, Z = 0.47. x2 = 16678.8
P(Z < (x1 - 15015)/3540) = 0.32, Z = -0.47, x1 = 13351.2