The Hill of Tara is located in south-central Meath not far from Dublin, Ireland. Tara is...

The Hill of Tara is located in south-central Meath not far from Dublin, Ireland. Tara is of great cultural and archaeological importance, since it is by legend the seat of the ancient high kings of Ireland. Magnetic surveying is one technique used by archaeologists to determine anomalies arising from variation 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 on the Hill of Tara. A random sample of 120 sites gave the readings shown.
Source: Tara: An Archaeological Survey, C. Newman, Royal Irish Academy, Dublin.

Approx. Magnetic SusceptibilityEstimated Probability50.35150.05250.05350.52450.03Approx. Magnetic Susceptibility515253545Estimated Probability0.350.050.050.520.03

(a) Find the expected value of the magnetic susceptibility, to one decimal place.
(b) Calculate the standard deviation of the discrete probability distribution to two decimal places.

Solutions

Expert Solution

Solution :

x	P(x)	x * P(x)	x2 * P(x)
5	0.35	1.75	8.75
15	0.05	0.75	11.5
25	0.05	1.25	31.25
35	0.52	18.2	637
45	0.03	1.35	60.75
Sum	1	23.3	749.25

(a)

Mean = = X * P(X) = 23.3

(b)

Standard deviation =

=X 2 * P(X) - 2

= 749.25 - 23.32

= 14.36

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