A normal distribution has a mean of -10.8 and a variance of 723.6. The probability that a value from this distribution will be between -25 and + 25 equals ________.
Answer(s): C
The standard deviation of the distribution equals sqrt(723.6) = 26.9. The z-value of -25 equals (-25 + 10.8)/26.9 = -0.53. The z-value of + 25 equals (25 + 10.8)/26.9 = + 1.33. Therefore, the probability that a number Y lies between -25 and + 25 is the same as the z-score lying between -0.53 and + 1.33. Using the Normal probability tables, we get P(z < 1.33) = 0.9082. Getting P(z < -0.53) can be tricky when the table given is only for positive values. To calculate the probability, use the fact that the standard normal distribution is symmetrical about zero.Hence, P(z < - 0.53) = P(z > 0.53) = 1.0 - 0.7019 = 0.2981. The probability that a number Y lies between -25 and + 25 is then given by P(-0.53 < z < 1.33) = P(z < 1.33) - P(z < -0.53) = 0.9082 - 0.2981 = 0.61.
If you buy an item for $1,500 and agree to pay for it with 36 monthly payments of $55.50, beginning next month, what annual interest rate, compounded monthly, are you being charged?
Answer(s): E
The interest rate returned by the calculator will be the periodic interest rate. It must be multiplied by the number of periods per year to have the correct answer. On the BAII Plus, press 36 N, 1500 PV, 55.50 +/- PMT, 0 FV, CPT I/Y. Then press x 12 = to see the answer. On the HP12C, press 36 n, 1500 PV, 55.50 CHS PMT, 0 FV, i.Then press 12 x to see the answer. Make sure the BAII Plus has the P/Y value set to 1.
The mean weight of trucks traveling on a particular section of I-475 is not known. A state highway inspector needs an estimate of the mean. He selects a random sample of 49 trucks passing the weighing station and finds the mean is 15.8 tons, with a standard deviation of the sample of 3.8 tons. What is the 95 percent interval for the population mean?
Answer(s): A
Interval estimate can be found from x_bar +/-z*s/(n^0.5). Here we have n = 49, x_bar = 15.8 and z = 1.96 (for 95%) and s = 3.8. Therefore 15.8 +/- 1.96*3.8/7 and we get 14.76 and 16.84.
A sample of size 100 is drawn from a population. The sample mean equals 35.2 and the variance of the sample equals 47.8. The 95% confidence interval for the population mean is given by:
Answer(s): D
If z is the z-value corresponding to the specified confidence level, the sample mean is M and the standard deviation is D in a sample size N, the confidence interval is specified as [M - z*D/sqrt(N), M + z*D/sqrt(N)]. In the present case, for the 95% confidence interval, z = 1.96. The sample standard deviation equals sqrt(47.8) = 6.91. Therefore, the confidence interval equals [35.2 - 1.96*6.91/sqrt(100), 35.2 - 1.96*6.91/sqrt(100)] = [33.85, 36.56]
Which of the following is correct about a probability distribution?
All describes properties of a probability distribution.
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