Ireland. Tara is of great cultural and archaeological importance, since it is by

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Ireland. Tara is of great cultural and archaeological importance, since it is by legend the seat of the ancient high kings of Ireland. For more information, see Tara: An Archaeological Survey, by Conor Newman, Royal Irish Academy, Dublin. Magnetic surveying is one technique used by archaeologists to determine anomalies arising from variations in magnetic susceptibility. Unusual changes in magnetic susceptibility might (or might not) indicate an important archaeological discovery. Let x be a random variable that represents a magnetic susceptibility (MS) reading for a randomly chosen site on the Hill of Tara. A random sample of 120 sites gave the readings shown in the table below. Magnetic Susceptibility Readings centimeter-gram-second 10-6 What is probability? A probability is a numerical measure greater than or equal to and less than or equal to that describes the likelihood that an event will occur. Probabilities closer toindicate that the event is more likely to occur. Probabilities closer to indicate that event is less likely to occur. the What do we mean by relative frequency as a probability estimate for events? A probability assignment based on relative frequency uses the formula, probability of event- relative frequencyfrequency disarabutionx where f is the frequency of the event occurrence in a sample of n observations What is the law of large numbers? How would the law of large numbers apply in this context? o The law of large numbers states that for any number of trials, the relative frequency is the same as the theoretical probability. If we took more and more readings, the relative frequencies would always be perfect estimates of the true probabilities. O The law of large numbers states that as the number of trials decreases, the relative frequency approaches the theoretical probability. If we took more and more readings, the relative frequencies would become less accurate estimates of the true probabilities. O The law of large numbers states that as the number of trials increases, the relative frequency approaches the theoretical probability. If we took more and more readings, the relative frequencies would become more accurate estimates of the true probabilities O The law of large numbers states that as the number of trials decreases, the relative frequency approaches the theoretical probability. If we took more and more readings, the relative frequencies would become more accurate estimates of the true probabilities. O The law of large numbers states that as the number of trials increases, the relative frequency approaches the theoretical probability. If we took more and more readings, the relative frequencies would become les accurate estimates of the true probabilities Need Help?

Explanation / Answer

(a) A probability is a numerical measure greater than or equal to 0 and less than or equal to 1

(b) A relative frequency is the fraction of times an answer occurs. To find the relative frequencies, divide each frequency by the total number of students in the sample

Relative frequenciescan be written as fractions, percents, or decimals.

Relative frequency = (number of trials that are successful) / (total number of trials)

RelativeFrequency= f / n

Here,

f is the number of times the data occurred in an observation
n  = total frequencies

(c) The law of large numbers is a principle of probability according to which the frequencies of events with the same likelihood of occurrence even out, given enough trials or instances. As the number of experiments increases, the actual ratio of outcomes will converge on the theoretical, or expected, ratio of outcomes.

the law of large numbers works better for larger samples.

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