Magnetic surveying is one technique used by archaeologists to determine anomalie

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.

0 x < 10

10 x < 20

20 x < 30

30 x < 40

40 x

For a site chosen at random, estimate the following probabilities.

(a)

P(0 x < 30)

(b)

P(10 x < 40)

(c)

P(x < 20)

(d)

P(x 20)

(e)

P(30 x)

(f)

P(x not less than 10)

(g)

P(0 x < 10 or 40 x)

(h)

P(40 x and 20 x)

Magnetic Susceptibility Readings,
centimeter-gram-second 106 (cmg 106) 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

Explanation / Answer

(a) P(0 x < 30) =0.3+0.4+0.1 =0.80

(b) P(10 x < 40) =0.4+0.1+0.15=0.65

(c) P(x < 20) =0.3+0.4 =0.7

(d) P(x >= 20) =1-P(x<20)=1-0.7 =0.3

e)P(30 x) =1-P(X<30) =-1-0.80 =0.20

f)P(x not less than 10) =1-P(X<10) =1-0.3 =0.70

g)P(0 x < 10 or 40 x) =0.3+0.05 =0.35

h)P(40 x and 20 x) =P(40<=x)=0.05

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