Answer:
a. E(x) = 3.730
b. c = 3.8475
c. 0.4308
Step-by-step explanation:
a.
Given
0 x < 3
F(x) = (x-3)/1.13, 3 < x < 4.13
1 x > 4.13
Calculating E(x)
First, we'll calculate the pdf, f(x).
f(x) is the derivative of F(x)
So, if F(x) = (x-3)/1.13
f(x) = F'(x) = 1/1.13, 3 < x < 4.13
E(x) is the integral of xf(x)
xf(x) = x * 1/1.3 = x/1.3
Integrating x/1.3
E(x) = x²/(2*1.13)
E(x) = x²/2.26 , 3 < x < 4.13
E(x) = (4.13²-3²)/2.16
E(x) = 3.730046296296296
E(x) = 3.730 (approximated)
b.
What is the value c such that P(X < c) = 0.75
First, we'll solve F(c)
F(c) = P(x<c)
F(c) = (c-3)/1.13= 0.75
c - 3 = 1.13 * 0.75
c - 3 = 0.8475
c = 3 + 0.8475
c = 3.8475
c.
What is the probability that X falls within 0.28 minutes of its mean?
Here we'll solve for
P(3.73 - 0.28 < X < 3.73 + 0.28)
= F(3.73 + 0.28) - F(3.73 + 0.28)
= 2*0.28/1.3 = 0.430769
= 0.4308 -- Approximated
Answer:
92
Step-by-step explanation:
= 3200 ÷ 35
= 91.43
round up to nearest whole number
= 92 km
Answer:
78.5
Step-by-step explanation:
The diameter (d) is equal to the radius x 2, so take half of d to get r. Use r (5) in the equation to get your answer.
A= 3.12 x 5^2
A= 78.5
Answer:
5 gallons of gas
Step-by-step explanation:
From the above question:
If:
80 miles = 4 gallons of gas
100 miles = x gallons of gas
Cross Multiply
80 × x = 100 × 4
x = 100 × 4/80
x = 5 gallons of gas
Therefore, Jackson would use 5 gallons of gas to get to Mount Highmore.
Answer:
The correct answer is 2 pi d
Step-by-step explanation:
