Question 1191862: 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.(use two decimal place for the mean, 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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