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 x 10¼ (cmg x 10-) Number of Readings 36 Magnetic Susceptibility Comment "cool" "neutral" "warm" OSx< 10 10 sx < 20 20 sx< 30 30 sx < 40 40 s x Estimated Probability 36/120 = 0.30 48/120 = 0.40 24/120 = 0.20 6/120 = 0.05 6/120 = 0.05 48 24 "very interesting" "hot spot" 6. 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. (a) Let us call "very interesting" a binomial success. Use the table above to find p, the probability of success on a single trial, where p = P(success) = P(30 sx < 40). (b) What is the expected value u and standard deviation o for the random variable r? (Round your standard deviation to three decimal places.) (c) What is the probability that you will find at least one "very interesting" reading in the 12 sites? (Round your answer to three decimal places.)
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 x 10¼ (cmg x 10-) Number of Readings 36 Magnetic Susceptibility Comment "cool" "neutral" "warm" OSx< 10 10 sx < 20 20 sx< 30 30 sx < 40 40 s x Estimated Probability 36/120 = 0.30 48/120 = 0.40 24/120 = 0.20 6/120 = 0.05 6/120 = 0.05 48 24 "very interesting" "hot spot" 6. 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. (a) Let us call "very interesting" a binomial success. Use the table above to find p, the probability of success on a single trial, where p = P(success) = P(30 sx < 40). (b) What is the expected value u and standard deviation o for the random variable r? (Round your standard deviation to three decimal places.) (c) What is the probability that you will find at least one "very interesting" reading in the 12 sites? (Round your answer to three decimal places.)
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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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.
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Transcribed Image Text:**Magnetic Surveying and Binomial Probability in Archaeology**
Magnetic surveying is a technique used by archaeologists to detect anomalies caused by variations in magnetic susceptibility, which may indicate significant archaeological discoveries. 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 provided the following readings:
**Table: Magnetic Susceptibility Readings (cmg × 10\(^{-6}\))**
| Magnetic Susceptibility | Number of Readings | Estimated Probability |
|-------------------------|--------------------|-----------------------|
| 0 \( \leq x < \) 10 ("cool") | 36 | 0.30 |
| 10 \( \leq x < \) 20 ("neutral") | 48 | 0.40 |
| 20 \( \leq x < \) 30 ("warm") | 24 | 0.20 |
| 30 \( \leq x < \) 40 ("very interesting") | 6 | 0.05 |
| 40 \( \leq x \) ("hot spot") | 6 | 0.05 |
A reading between 30 and 40 is classified as "very interesting." Let's assume you take readings at \(n = 12\) sites randomly. Let \(r\) be a binomial random variable representing the number of "very interesting" readings from these 12 sites.
**Questions**
(a) **Binomial Success**
- Calculate \(p\), the probability of success for a single trial, where \(p = P(30 \leq x < 40)\).
(b) **Expected Value and Standard Deviation**
- What are the expected value \(\mu\) and standard deviation \(\sigma\) for the random variable \(r\)?
- Round \(\sigma\) to three decimal places.
(c) **Probability of At Least One "Very Interesting" Reading**
- What is the probability of obtaining at least one "very interesting" reading from the 12 sites?
- Round your answer to three decimal places.
(d) **Probability of Fewer Than Three "Very Interesting" Readings**
- What is the probability of finding fewer than three "very interesting" readings in the 12 sites?
- Round your answer to three decimal places.
Utilize the table to analyze the probabilities and
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