(a)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 24 24/120 = 0.20 "neutral" 10 ≤ x < 20 60 60/120 = 0.50 "warm" 20 ≤ x < 30 18 18/120 = 0.15 "very interesting" 30 ≤ x < 40 12 12/120 = 0.10 "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) = (b) 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 12 12/120 = 0.10 "very interesting" 30 ≤ x < 40 18 18/120 = 0.15 "hot spot" 40 ≤ x 6 6/120 = 0.05 Consider the midpoint of each interval. Assign the value 45 as the midpoint for the interval 40 ≤ x. The midpoints constitute the sample space for a discrete random variable. Using the table above, compute the expected value μ and the standard deviation σ. (Round your standard deviation σ to three decimal places) μ = σ =

(a)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 24 24/120 = 0.20 "neutral" 10 ≤ x < 20 60 60/120 = 0.50 "warm" 20 ≤ x < 30 18 18/120 = 0.15 "very interesting" 30 ≤ x < 40 12 12/120 = 0.10 "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) = (b) 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 12 12/120 = 0.10 "very interesting" 30 ≤ x < 40 18 18/120 = 0.15 "hot spot" 40 ≤ x 6 6/120 = 0.05 Consider the midpoint of each interval. Assign the value 45 as the midpoint for the interval 40 ≤ x. The midpoints constitute the sample space for a discrete random variable. Using the table above, compute the expected value μ and the standard deviation σ. (Round your standard deviation σ to three decimal places) μ = σ =

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Magnetic Susceptibility Readings, centimeter-gram-second ✕ 10⁻⁶ (cmg ✕ 10⁻⁶)
Comment	Magnetic Susceptibility	Number of Readings	Estimated Probability
"cool"	0 ≤ x < 10	24	24/120 = 0.20
"neutral"	10 ≤ x < 20	60	60/120 = 0.50
"warm"	20 ≤ x < 30	18	18/120 = 0.15
"very interesting"	30 ≤ x < 40	12	12/120 = 0.10
"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)

(b) 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	12	12/120 = 0.10
"very interesting"	30 ≤ x < 40	18	18/120 = 0.15
"hot spot"	40 ≤ x	6	6/120 = 0.05

Consider the midpoint of each interval. Assign the value 45 as the midpoint for the interval

40 ≤ x.

The midpoints constitute the sample space for a discrete random variable. Using the table above, compute the expected value μ and the standard deviation σ. (Round your standard deviation σ to three decimal places)

μ =
σ =

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