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)...


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. Letx 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 <>

2424/120 = 0.20
"neutral"
10 ≤ x <>

6060/120 = 0.50
"warm"
20 ≤ x <>

1212/120 = 0.10
"very interesting"
30 ≤ x <>

1818/120 = 0.15
"hot spot"
40 ≤ x

66/120 = 0.05


Suppose a reading between 30 and 40 is called "very interesting" from an archaeological point of view. Let us say you take readings at


n = 12

 sites chosen at random. Letr be a binomial random variable that represents the number of "very interesting" readings from these 12 sites.


(a) Let us call "very interesting" a binomial success. Use the table above to findp, the probability of success on a single trial, where
p = P(success) = P(30 ≤ x <>






(b) What is the expected value μ and standard deviation σ for the random variabler? (Round your standard deviation to three decimal places.)












μ =
σ =


(c) What is the probability that you will findat least one "very interesting" reading in the 12 sites? (Round your answer to three decimal places.)




(d) What is the probability that you will findfewer than three "very interesting" readings in the 12 sites? (Round your answer to three decimal places.)
Jun 05, 2022
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