Answer:
E(X) = 41.196
Var(X) = 17.975
E(Y) = 40.75
Var(Y) = 9.922
Step-by-step explanation:
40 + 41 + 35 + 47 = 163
The probability that a student was on the bus is proportional to how many students were on the bus. So, for bus a, its = 40/163 ; for bus b, it's = 41/163 ;for bus c, it's 35/163= ;for bus d, it's = 47/163
A) E(X) = 40(40/163) + 41(41/163) + 35(35/163) + 47(47/163)
E(X) = 6715/163
E(X) = 41.196
B) Var(X) = [(40 - 41.196)²•(40/163)] + [(41 - 41.196)²•(41/163)] + [(35 - 41.196)²•(35/163)] + [(47 - 41.196)²•(47/163)]
Var(X) = (1.430416 + 1.575056 + 1343.66456 + 1583.261552)/163
Var(X) = 2929.931584/163
Var(X) = 17.975
C) The bus driver has a 1/4 probability on being on any of the buses. Thus,
E(Y) = 163/4
E(Y) = 40.75
D) Var(Y) = (40.75 - 40)²/4 + (40.75 - 41)²/4 + (40.75-35)²/4 + (40.75-47)²/4
Var(Y) = 0.140625 + 0.015625 + 9.765625
Var(Y) = 9.922
-2x + 3b > 5
Subtract 3b from both sides:
-2x > 5-3b
Divide by -2 on both sides. (When you are dividing by a negative number, the greater than symbol will be reversed to a less than symbol):
x < (5-3b)/(-2)
There are 5 blue shirts and only one is big, so the probability would be 1/12. The percentage would be approximately 8%
3 7/10 + 5 4/10 = 8 11/10 = 9 1/10
so estimate = 9
actual answer = 9 1/10
yes, his answer is reasonable
90+30=120
180-120=60
The measurement for angle G is 60 degrees.
And for angle J is the same as 90+30 which equals 120 degrees.