A statistic is the measure of some characteristic of a population.
What is false. A parameter is the measure of some characteristic of a population. A statistic describes a sample.
100
What is the addition law of probability for mutually exclusive events?
What is Probability of A union B = P(A) + P(B)
100
How many ways can three items be selected from a group of six items if order doesn't matter?
What is 20 ways (using combinations formula)?
100
Test the following function to determine whether it is a probability function. List and sketch the probability distribution. f(x) = (x2+5)/50 for x = 1, 2, 3, 4
What is: f(x) is a probability function. The probabilities are greater than or equal to 0, and the sum of f(x)'s is 1.
100
Consider a sample with data values of 53, 55, 70, 58, 64, 57, 53, 69, 57, 68, and 53. Compute the mean, median, and mode.
What is 59.7, 57, and 53?
200
One way to identify quantitative variables measured on a ratio scale is whether or not zero means the absence of what is being measured.
What is true. Quantitative variables measured on an interval scale do not have a true 0. One example is Fahrenheit temperature.
200
For the experiment of flipping a coin 5 times, what is the probability of getting exactly 3 heads?
What is 10/32?
200
Tires salvaged from a train wreck are on sale at the Getrich Tire Company. Of the 15 tires offered, 5 have internal damage and 10 are damage free. You randomly selected and purchased 2 of these tires. What is the probability that the tires you purchased are both damage free?
What is P(both damage free) = (10/15)*(9/14) = 0.429
200
Find the mean of the probability function f(x) = x/10 for x = 1, 2, 3, 4
What is 1*.1+2*.2+3*.3+4*.4 = 3.0
200
Consider a sample with the data values of 10, 20, 12, 17, and 16. Compute the variance and standard deviation.
What is 16, 4.
300
The standard deviation for the set of values 2, 2, 2, 2, and 2 is 2.
What is false. Since standard deviation is a measure of variability, and there is no variability in the data, the standard deviation is 0.
300
What is the Empirical Rule?
What is for data having a bell-shaped distribution: Approximately 68% of the data values will be within 1 s. Approximately 95% of the data values will be within 2 s.
Approximately 100% of the data values will be within 3 s.
300
Assume you have a regular deck of 52 cards and 4 suits. What is the probability that you will draw a pair of 2's from the deck (without replacement)?
What is 4/52 * 3/51 = 1/13 * 1/17 = 1/221
300
Find the mean and standard deviation of the random variable x for the number of tails seen in 50 tosses of a quarter.
What is ยต = np = 50*(0.5) = 25.0; standard deviation =
square root of (np(1-p) = 50*(0.5)*(0.5) = 3.5355 = 3.5 since this is a binomial random variable.
300
The following data are the yields (in pounds) of hops:
3.9, 3.4, 5.1, 2.7, 4.4, 7.0, 5.6, 2.6, 4.8, 5.0. Find the first and third quartiles.
What is 3.4 and 5.1?
400
If 2 events are mutually exclusive, they are also independent.
What is false. Two events with nonzero probabilities cannot be both mutually exclusive and independent. If one mutually exclusive event is known to occur, the other cannot occur; thus, the probability of the other event occurring is known to be zero. The occurrence of one impacts the probability of the other. They are therefore dependent.
400
If the correlation coefficient between 2 variables is 3, what does that mean?
What is it means you calculated incorrectly. The correlation coefficient ranges from -1 to 1.
400
Assume you have a regular deck of 52 cards with 4 suits. What is the probability of drawing 2 cards of the same suit?
What is 52/52 * 12/51 = 12/51?
400
A box contains 10 items, of which 3 are defective and 7 are nondefective. Two items are selected without replacement, and x is the number of defective items in the sample of two. Is x a binomial random variable? Why or why not?
What is no. If x is the random variable n(defective), then success is defective. On the first selection, P(defective) = 3/10. However, the P(defective) changes for the next selection: it is either 3/9 or 2/9 depending on whether or not the first selection resulted in a defective or not. Since the probability of defective changes, the trials are not independent. Thus, the experiment is not binomial.
400
An exam produced grades with a mean score of 74.2 and standard deviation of 11.5. Find the z-score for a test score of 54.
What is for x = 54, z = (54 - 74.2)/11.5 = -1.76
500
The length of the cord on an electrical appliance is an example of a discrete random variable.
What is False. A discrete random variable can assume a countable number of values. A continuous random variable can assume an uncountable number of values. They are measurements that can assume any value along an interval. The length of the cord is an example of a continuous random variable. It answers, "How much" rather than "How many."
500
List the scales of measurement for variables and describe the information contained in each one.
What is nominal (labels or names identify attribute or category); ordinal (information contained in nominal plus order or rank is meaningful); interval (information contained in ordinal plus distance between ranks is meaningful); ratio (information contained in interval plus the ratio of 2 values is meaningful and zero means nothing exists.)
500
The probability that a certain door is locked is 0.6. The key to the door is one of five unidentified keys hanging on a key rack. You randomly select two keys before approaching the door. What is the probability that you can open the door without returning for another key? (Draw a tree diagram in your answer.)
What is P(open door) = 0.4 + (0.6)*(1/5) + (0.6)*(4/5)*(1/4)
= 0.4 + 0.12 + 0.12 = 0.64
500
R&B songs account for 60% of radio's top 100 hits. A new radio station named Fickle plays all types of music from the list of the topp 100 hits including R&B, pop, rock, and country. In the next randomly selected group of 14 songs, what is the probability that more than seven songs are R&B songs?
What is P(x > 7*B(n = 14, p = 0.60)) = (0.207 + 0.207 + 0.155 +
0.085 + 0.032 + 0.007 + 0.001) = 0.694
500
An exam produced grades with a mean score of 74.2 and a standard deviation of 11.5. According to Chevyshev's Theorem, at most what percentage of scores will be above 94.44 and below 54?