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 at an archaeological research location. A random sample of 120 sites gave the readings shown in the table below. Magnetic Susceptibility Readings, centimeter-gram-second ✕ 10−6 (cmg ✕ 10−6) Comment Magnetic Susceptibility Number of Readings Estimated Probability "cool" 0 ≤ x < 10 30 30/120 = 0.25 "neutral" 10 ≤ x < 20 54 54/120 = 0.45 "warm" 20 ≤ x < 30 24 24/120 = 0.20 "very interesting" 30 ≤ x < 40 6 6/120 = 0.05 "hot spot" 40 ≤ x 6 6/120 = 0.05 Suppose you are working in a "warm" region in which all MS readings are 20 or higher. In this same region, what is the probability that you will find a "hot spot" in which the readings are 40 or higher? Use conditional probability to estimate P(40 ≤ x | 20 ≤ x). (Round your answer to three decimal places.) P(40 ≤ x | 20 ≤ x) =
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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 at an archaeological research location. A random sample of 120 sites gave the readings shown in the table below.
| Magnetic Susceptibility Readings, centimeter-gram-second ✕ 10−6 (cmg ✕ 10−6) |
|||
| Comment | Magnetic Susceptibility |
Number of Readings |
Estimated |
| "cool" |
0 ≤ x < 10
|
30 | 30/120 = 0.25 |
| "neutral" |
10 ≤ x < 20
|
54 | 54/120 = 0.45 |
| "warm" |
20 ≤ x < 30
|
24 | 24/120 = 0.20 |
| "very interesting" |
30 ≤ x < 40
|
6 | 6/120 = 0.05 |
| "hot spot" |
40 ≤ x
|
6 | 6/120 = 0.05 |
Suppose you are working in a "warm" region in which all MS readings are 20 or higher. In this same region, what is the probability that you will find a "hot spot" in which the readings are 40 or higher? Use conditional probability to estimate
(Round your answer to three decimal places.)
=
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