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 10-6 (cmg × 10-6) Magnetic Susceptibility Number of Readings Estimated Probability Comment "cool" Osx< 10 24 24/120 = 0.20 60/120 = 0.50 18/120 = 0.15 "neutral" 10 sx< 20 60 "warm" 20 sx< 30 18 "very interesting" "hot spot" 30 sx< 40 12 12/120 = 0.10 6/120 = 0.05 40 sx n USE SALT Consider a binomial setting in which "neutral" is defined to be success. So, p = P(success) = P(10 s x < 20). Suppose n = 55 geomagnetic readings are taken. Let r be a binomial random variable that represents the number of "neutral" geomagnetic readings. (a) We want to approximate the binomial random variabler by a normal variable x. Is this appropriate? What requirements must be satisfied before we can do this? Do you think these requirements are satisfied in this case? Explain. O Yes, it is appropriate since n 2 30. O No, it is not appropriate since at least one of the criteria np > 5 and ng > 5 are not satisfied. O No, it is not appropriate since at least one of the criteria n 2 100 or np < 10 are not satisfied. O Yes, it is appropriate since the criteria n 2 100 or np < 10 are are both satisfied. O Yes, it is appropriate since the criteria np > 5 and ng > 5 are both satisfied. (b) Use the normal distribution to approximate the probability that there will be at least 20 "neutral" readings out of these 55 trials. (Round your answer to four 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 10-6 (cmg × 10-6) Magnetic Susceptibility Number of Readings Estimated Probability Comment "cool" Osx< 10 24 24/120 = 0.20 60/120 = 0.50 18/120 = 0.15 "neutral" 10 sx< 20 60 "warm" 20 sx< 30 18 "very interesting" "hot spot" 30 sx< 40 12 12/120 = 0.10 6/120 = 0.05 40 sx n USE SALT Consider a binomial setting in which "neutral" is defined to be success. So, p = P(success) = P(10 s x < 20). Suppose n = 55 geomagnetic readings are taken. Let r be a binomial random variable that represents the number of "neutral" geomagnetic readings. (a) We want to approximate the binomial random variabler by a normal variable x. Is this appropriate? What requirements must be satisfied before we can do this? Do you think these requirements are satisfied in this case? Explain. O Yes, it is appropriate since n 2 30. O No, it is not appropriate since at least one of the criteria np > 5 and ng > 5 are not satisfied. O No, it is not appropriate since at least one of the criteria n 2 100 or np < 10 are not satisfied. O Yes, it is appropriate since the criteria n 2 100 or np < 10 are are both satisfied. O Yes, it is appropriate since the criteria np > 5 and ng > 5 are both satisfied. (b) Use the normal distribution to approximate the probability that there will be at least 20 "neutral" readings out of these 55 trials. (Round your answer to four decimal places.)
MATLAB: An Introduction with Applications
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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 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 10-6 (cmg x 10-6)
Magnetic
Susceptibility
Osx < 10
10 sx < 20
Number of
Readings
Estimated
Comment
Probability
"cool"
24
24/120 = 0.20
60/120 = 0.50
"neutral"
60
"warm"
20 sx < 30
18
"very interesting"
"hot spot"
30 sx < 40
40 < x
18/120 = 0.15
12/120 = 0.10
6/120 = 0.05
12
6
n USE SALT
Consider a binomial setting in which "neutral" is defined to be a success. So, p = P(success) = P(10 s x < 20). Suppose n = 55 geomagnetic readings are taken. Let r be a
binomial random variable that represents the number of "neutral" geomagnetic readings.
(a) We want to approximate the binomial random variable r by a normal variable x. Is this appropriate? What requirements must be satisfied before we can do this? Do
you think these requirements are satisfied in this case? Explain.
O Yes, it is appropriate since n 2 30.
O No, it is not appropriate since at least one of the criteria np > 5 and ng > 5 are not satisfied.
No, it is not appropriate since at least one of the criteria n 2 100 or np < 10 are not satisfied.
Yes, it is appropriate since the criteria n 2 100 or np < 10 are are both satisfied.
O Yes, it is appropriate since the criteria np > 5 and ng > 5 are both satisfied.
(b) Use the normal distribution to approximate the probability that there will be at least 20 "neutral" readings out of these 55 trials. (Round your answer to four
decimal places.)
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