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 36 36/120 = 0.30 "neutral" 10 ≤ x < 20 48 48/120 = 0.40 "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 a reading between 30 and 40 is called "very interesting" from an archaeological point of view. Let us say you take readings at n = 12 sites chosen at random. Let r be a binomial random variable that represents the number of "very interesting" readings from these 12 sites. (b) What is the expected value μ and standard deviation σ for the random variable r? (Round your standard deviation to three decimal places.) μ = σ =
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 Probability |
| "cool" |
0 ≤ x < 10
|
36 | 36/120 = 0.30 |
| "neutral" |
10 ≤ x < 20
|
48 | 48/120 = 0.40 |
| "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 a reading between 30 and 40 is called "very interesting" from an archaeological point of view. Let us say you take readings at
sites chosen at random. Let r be a binomial random variable that represents the number of "very interesting" readings from these 12 sites.
(b) What is the
| μ = | |
| σ = |
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