Question 1191861: Your mother said, if in the 3rd Quarter your grade in Math is 95 and above, she will add Php50 to your daily allowance, Php40 if 90 - 94, Php30 if 85 - 89, Php20 if 80-84, but will decrease your allowance by Php15 if your grade is 79 and below. If the probability of getting 95 and above is 17%, 90 - 94 is 15%, 85 - 89 is 28%, 80 - 84 is 25%, and 15% if 79 and below. Construct the probability distribution of the additional allowances your mother will give you. Find the expected value, variance, and standard deviation
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! <79--prob. 0.15, - 15, expected value is -2.25 Php, the product.
80-84--prob 0.25 +20, expected value is 5.00
85-89--prob. 0.28 +30, expected value is 8.40
90-94 prob. 0.15 +40, expected value is 6.00
>=95 prob. 0.17 (1.00-all the other probabilities) +50, expected value is 8.5
add the expected values to get 25.65 Php
variance is sum of (value-expected)^2*probablity
27.90^2*0.15=116.76
20.65^2*0.25=106.61
17.25^2*0.28=83.32
19.25^2*0.15=55.58
17.15^2*0.17=50.00
Add those to get 412.26 Php^2, the variance.
sd= sqrt (V)=20.30 Php
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