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 a "hot spot" is a site with a reading of 40 or higher. (a) In a binomial setting, let us call success a "hot spot." Use the table above to find p = P(success) = P(40 ≤ x) for a single trial. (b) Suppose you decide to take readings at random until you get your first "hot spot." Let n be a random variable representing the trial on which you get your first "hot spot." Use the geometric probability distribution to write out a formula for P(n). P(n) = (c) What is the probability that you will need more than four readings to find the first "hot spot"? Compute P(n > 4). (Round your answer to three decimal places.)

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Description: 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

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

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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 a "hot spot" is a site with a reading of 40 or higher.

(a) In a binomial setting, let us call success a "hot spot." Use the table above to find

p = P(success) = P(40 ≤ x)

for a single trial.

(b) Suppose you decide to take readings at random until you get your first "hot spot." Let n be a random variable representing the trial on which you get your first "hot spot." Use the geometric probability distribution to write out a formula for

P(n).

P(n) =

P(n > 4).

(Round your answer to three decimal places.)

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