The probability that a value from a normal distribution will be less than 4 equals 83%. If the distribution has a mean of 2.2, the standard deviation of the distribution must be:
Answer(s): C
Using the Normal probability tables, the z-value of the observation, X, which can be exceeded with a probability of 17% equals 0.955. We are given that X = 4. Now, the z-value of a selected observation, X, from a normal distribution with mean M and standard deviation S equals z = (X-M)/S. Therefore, 0.955 = (4 - 2.2)/S. This gives S = 1.885.
The significance level in hypothesis testing refers to the probability that we will:
Answer(s): B
Note that the significance level is the same as the probability of making a Type I error. A Type I error refers to the event that we will reject the null when, in fact, it is true. Clearly, lower significance levels are better, all else equal.
What annual simple interest rate would cause a $105 deposit to grow to $125 in 15 months?
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 20 (125 - 105). Note also that the time component T of the formula is 15/12. On the BAII Plus, press 20 divide 105 divide 15 x 12 = to see the answer. On the HP12C, press 20 ENTER 105 divide 15 divide 12 x to see the answer.
How many monthly payments of $50, beginning next month, are needed to pay off a debt of $700, if interest accrues at 8% per year, compounded monthly?
Answer(s): E
On the BAII Plus, press 8 divide 12 = I/Y, 700 PV, 50 +/- PMT, 0 FV, CPT N. On the HP12C, press 8 ENTER 12 divide i, 700 PV, 50 CHS PMT, 0 FV, n. Note that the HP12C will display 15 as the answer. Make sure the BAII Plus has the P/Y value set to 1.
What quarterly deposit do you need to make each quarter, starting next quarter, over the next 10 years in order to have a balance of $15,000 in your account, assuming the account starts with $1,000 in it and that the interest rate is 6% per year, compounded quarterly?
Answer(s): A
There are 40 quarters in 10 years (10 x 4 =). The payment to be solved for as well as the original $1,000 balance can be viewed as deposits into the account and hence given the same sign. The $15,000 amount at the end of the timeframe should be of the opposite sign. On the BAII Plus, press 40 N, 6 divide 4 = I/Y, 1000 PV, 15000 +/- FV, CPT PMT. On the HP12C, press 40 n, 6 ENTER 4 divide i, 1000 PV, 15000 CHS FV, PMT.Note that the answer will be displayed as a negative number. Make sure the BAII Plus has the value of P/Y set to 1.
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