An automatic machine inserts mixed vegetables into a plastic bag. Past experience revealed that some packages were underweight and some were overweight, but most of them had satisfactory weight.Weight % of TotalUnderweight 2.5Satisfactory 90.0Overweight 7.5What is the probability of selecting and finding that all three of them are overweight?
Answer(s): A
P(all three overweight)=0.075*0.075*0.075 = 0.0004218.
Variables X and Y are perfectly negatively correlated. Given only this information, if you run a regression of Y against X, which of the following is/are true?
Answer(s): E
If Y = aX + b, then X and Y are perfectly negatively correlated for any value of b and any negative value of a.Hence, given the information in the question, the slope must be negative but not necessarily equal to 1 and the intercept term cannot be determined. Since the correlation coefficient is 1, R-square is also 1, as expected, since all the variation in Y can be explained by variation in X. Note that the percentage of unexplained variance equals zero.
If you make an initial deposit $500 now into an account, an additional deposit of $800 in 2 years, and a final deposit of $300 in 4 years, how much is in your account in 5 years? Assume the account earns interest at 8% per year, compounded annually.
Answer(s): C
Solve this question by working several compound interest problems, moving each dollar amount over to year 5.On the BAII Plus, press 5 N, 8 I/Y, 500 PV, 0 PMT, CPT FV, which yields $734.66. Then press STO 1, 3 N, 800 PV, CPT FV, which yields $1,007.77. Then press + RCL 1 = STO 1. Then press 1 N, 300 PV, CPT FV, which yields $324.00. Then press + RCL 1 = to see the answer. On the HP12C, press 5 n, 8 i, 500 PV, 0 PMT, FV.Then press STO 1, 3 n, 800 PV, FV. Then press RCL 1 + STO 1. Then press 1 n, 300 PV, FV. Then press RCL 1 + to see the answer. Note that the answer will be displayed as a negative number. Also note that the value of "N" for each dollar amount is based on the distance from year 5. Make sure the BAII Plus has the P/Y value set to 1.
What simple annual interest rate would cause a $110 deposit to grow to $120 in 2 years?
To solve this question, we have to rearrange the simple interest formula, I=PRT so that the R is by itself. Note that the I (interest) is equal to 10 (120 - 100). On the BAII Plus, press 10 divide 110 divide 2 = to see the answer. On the HP12C, press 10 ENTER 110 divide 2 divide to see the answer.
The probability that events A and B do not occur simultaneously equals 0.77. The probability of neither A nor B occurring equals 0.38. If P(A) equals 0.26, the probability of B occurring equals ________.
Answer(s): B
The probability that events A and B do not occur simultaneously equals one minus the probability that events A and B occur simultaneously. Thus,P(A and B) = 1 - 0.77 = 0.23.The probability of neither A nor B occurring equals one minus the probability of either A or B occurring. Thus, P (A or B) = 1 - 0.38 = 0.62.Now, P(A or B) = P(A) + P(B) - P(A and B). Therefore, P(B) = P(A or B) - P(A) + P(A and B) = 0.62 - 0.26 + 0.23 = 0.59.
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