(1) 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.) (2) Would the Poisson approximation to the binomial not be appropriate in this case? Explain.

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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,
-6
centimeter-gram-second x 10
Magnetic
(cmg x 10-6)
Number of
Estimated
Susceptibility
0 < x < 10
Comment
Readings
24
Probability
= 0.20
"cool"
"neutral"
"warm"
24/120
60/120 = 0.50
12/120 = 0.10
18/120 = 0.15
= 0.05
10 < x < 20
60
12
18
20 < x < 30
"very interesting"
"hot spot"
30 < x < 40
40 < x
6/120 :
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. Letr be a binomial random variable that represents the number of "neutral" geomagnetic
readings.
(1) 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.)
(2) Would the Poisson approximation to the binomial not be appropriate in this case? Explain.
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 np > 5 and nq > 5 are both satisfied.
Yes, it is appropriate since n 2 30.
O Yes, it is appropriate since the criterian > 100 and np < 10 are are both satisfied.
No, it is not appropriate since at least one of the criteria np > 5 and nq > 5 are not satisfied.
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, -6 centimeter-gram-second x 10 Magnetic (cmg x 10-6) Number of Estimated Susceptibility 0 < x < 10 Comment Readings 24 Probability = 0.20 "cool" "neutral" "warm" 24/120 60/120 = 0.50 12/120 = 0.10 18/120 = 0.15 = 0.05 10 < x < 20 60 12 18 20 < x < 30 "very interesting" "hot spot" 30 < x < 40 40 < x 6/120 : 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. Letr be a binomial random variable that represents the number of "neutral" geomagnetic readings. (1) 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.) (2) Would the Poisson approximation to the binomial not be appropriate in this case? Explain. 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 np > 5 and nq > 5 are both satisfied. Yes, it is appropriate since n 2 30. O Yes, it is appropriate since the criterian > 100 and np < 10 are are both satisfied. No, it is not appropriate since at least one of the criteria np > 5 and nq > 5 are not satisfied.
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