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. Arandom sample of 120 sites gave the readings shown in the table below.Magnetic Susceptibility Readings,centimeter-gram-second x 10-6MagneticSusceptibility0 < x < 1010 < x < 20(cmg x 10-6)Number ofEstimatedCommentReadings24Probability24/120 = 0.2060/120 = 0.5012/120 =18/1206/120 ="cool""neutral""warm"6020 < x < 30120.10"very interesting""hot spot"30 < x < 4040 < x18= 0.156.n USE SALTConsider a binomial setting in which "neutral" is defined to be a success. So, p = P(success) = P(10 < x < 20). Suppose n = 45 geomagnetic readings are taken. Let r be a binomial random variable%3Dthat 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 theserequirements are satisfied in this case? Explain.O No, it is not appropriate since at least one of the criteria np > 5 and ng > 5 are not satisfied.Yes, it is appropriate since n 2 30.Yes, it is appropriate since the criteria np > 5 and ng > 5 are both 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 > 100 or np < 10 are are both satisfied.(b) Use the normal distribution to approximate the probability that there will be at least 17 "neutral" readings out of these 45 trials. (Round your answer to four decimal places.)(c) Would the Poisson approximation to the binomial not be appropriate in this case? Explain.

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Consider a binomial setting in which "neutral" is defined to be a success. So, p = P(success) = P(10 s x < 20). Suppose n = 45 geomagnetic readings are taken. Let r be a binomial random variable hat 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 No, it is not appropriate since at least one of the criteria np > 5 and ng > 5 are not satisfied. O Yes, it is appropriate since n2 30. O Yes, it is appropriate since the criteria np > 5 and ng > 5 are both 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. (b) Use the normal distribution to approximate the probability that there will be at least 17 "neutral" readings out of these 45 trials. (Round your answer to four decimal places.) (c) Would the Poisson approximation to the binomial not be appropriate in this case? Explain.

Consider a binomial setting in which "neutral" is defined to be a success. So, p = P(success) = P(10 s x < 20). Suppose n = 45 geomagnetic readings are taken. Let r be a binomial random variable hat 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 No, it is not appropriate since at least one of the criteria np > 5 and ng > 5 are not satisfied. O Yes, it is appropriate since n2 30. O Yes, it is appropriate since the criteria np > 5 and ng > 5 are both 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. (b) Use the normal distribution to approximate the probability that there will be at least 17 "neutral" readings out of these 45 trials. (Round your answer to four decimal places.) (c) Would the Poisson approximation to the binomial not be appropriate in this case? Explain.

MATLAB: An Introduction with Applications

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Author:Amos Gilat

Publisher:Amos Gilat

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Concept explainers

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.

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Question

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
Magnetic
Susceptibility
0 < x < 10
10 < x < 20
(cmg x 10-6)
Number of
Estimated
Comment
Readings
24
Probability
24/120 = 0.20
60/120 = 0.50
12/120 =
18/120
6/120 =
"cool"
"neutral"
"warm"
60
20 < x < 30
12
0.10
"very interesting"
"hot spot"
30 < x < 40
40 < x
18
= 0.15
6.
n USE SALT
Consider a binomial setting in which "neutral" is defined to be a success. So, p = P(success) = P(10 < x < 20). Suppose n = 45 geomagnetic readings are taken. Let r be a binomial random variable
%3D
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 No, it is not appropriate since at least one of the criteria np > 5 and ng > 5 are not satisfied.
Yes, it is appropriate since n 2 30.
Yes, it is appropriate since the criteria np > 5 and ng > 5 are both 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 > 100 or np < 10 are are both satisfied.
(b) Use the normal distribution to approximate the probability that there will be at least 17 "neutral" readings out of these 45 trials. (Round your answer to four decimal places.)
(c) Would the Poisson approximation to the binomial not be appropriate in this case? Explain.

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