Consider the following data set: Monthly (in thousands) payment of employees at

Question

Consider the following data set: Monthly (in thousands) payment of employees at company ABC. Find 5, 5, 6, 6, 7, 8, 8, 8, 9, 12, 12, 16, 18, 22, 24, 26, 27, 28, 40, 42, 50 the Outliers The XYZ association has 100 members. 25 of the members are Mexican, 32 of the members are Catholic and 8 of the members are both Mexican and Catholic. If you randomly select one person from this association what is the probability that (a) The person is Mexican or Catholic (b) The person is Mexican but not Catholic (c) The person is neither Mexican or Catholic (d) If the person selected is Mexican that she/he is Catholic (d) If the person selected is Not Mexican that she/he is Catholic (e) Are the events Mexican and Catholic independent? Explain

Explanation / Answer

Solution:-

Monthly payment of employees at company ABC.

Given data, 5,5,6,6,7,8,8,8,9,12,12,16,18,22,24,26,27,28,40,42,50

The outliers are:-

An outlier in a distribution is a number that is more than 1.5 times the length of the box away from either the lower or upper quartiles. Specically, if a number is less than Q1 - 1.5×IQR or greater than Q3 + 1.5×IQR, then it is an outlier.

UB = 26 + 1.5(18) = 53

LB = 8 - 1.5 (18) = -19

Therefore, here in the given data, we have NONE outliers.

2). Total members = 100

Mexican = 25

P(M) = 25/100 = 0.25

Catholic = 32

P(C) = 32/200 = 0.32

Members of Mexico and Catholic = 8

P(C and M) = 8/100 = 0.08

a) P(M or C) = P(M) + P(C) - P(M and C)

= 0.25 + 0.32 - 0.08 = 0.49

b) P(M or Cbar) = 0.17

c). P(1 - P(M or C)) = 0.51

d) P(C I M) = P(C and M) / P(M) = 0.08 / 0.25 = 0.32

e) P(Mbar I C) = P(Mbar and C) / P(M) = 0.96

f) Yes, the two ecents are not independent.

As the two events are independent if the result of the second event is not affected by the result of the first event. If A and B areindependent events, the probability of both events occurring is the product of the probabilities of the individual events.

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