4 (5 pts) Among my friends, 60% think I am reasonable, and friends who think I 2

Question

4 (5 pts) Among my friends, 60% think I am reasonable, and friends who think I 2 40% think I am not. Among the am reasonable, 70% support my new proposal on the community service 20% support my new proposal on the community service and the rest does not suppon the friend supports my the rest does not support the proposal. Amiong the friends who think 1 am not teasonable proposal. If I select a friend at random, what is the probability that the proposal? centimeters). Find the probability that the mcan of randomly selécted four peuplo from the area is between 146 and 150 centimeters 5 (S pts) The heights of people in an area follows a normal distribution N(150, 16) n

Explanation / Answer

Question 4:

Here, we are given that:

P( reasonable ) = 0.6, P( not reasonable ) = 0.4

P( support | reasonable ) = 0.7
P( no support | reasonable ) = 0.3

P( support | not reasonable ) = 0.2
P( no support | not reasonable ) = 0.8

Using law of total addition, we get here:

P( support ) = P( support | reasonable ) P( reasonable ) + P( support | not reasonable )  P( not reasonable )

P( support ) = 0.7*0.6 + 0.2*0.4 = 0.42 + 0.08 = 0.50

Therefore 0.50 is the required probability here.

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