This is best done using a Venn Diagram.
Given:
Probability that he gets into NYPD is 0.60
Probability that he gets into CSI is 0.70
Probability that he gets into both is 0.40
Probability that he gets into ONLY NYPD? 0.60 - 0.40 = 0.20
Probability that he gets into ONLY CSI? 0.70 - 0.40 = 0.30
Sum of the numbers in the set: 42+37+32+29+20 =160
Current mean: 160/5 = 32
Median = the valvue of the middle = 32.
New mean: 32+10= 42.
Sum of numbers in the new set = 42*8 = 336
Difference: 336 - 160 = 176
I want to include 32, so that the new median stays in 32.
So the other two numbers must add 176 - 32 = 144
I will use a smaller number than 32 and the other greater (again in order to keep the same median.
I will choose 28 and 144 - 28 = 116.
So my three new numbers are 28, 32 and 116 and the new set is {116, 42, 37, 32, 32, 29,28, 20}
Checking:
Sum of the terms: 116+42+37+32+32+29+28+20 = 336
Mean = 336 / 8 = 42, which is 10 more than the original mean.
And the new median is (32+32)/2 = 32. The same of the original set.
Answer:
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Step-by-step explanation: