Answer:
Wow - you are asking a LOT of questions. The Monthly Payment Formula is really tricky so I'll solve that for you.
The time of the loan = 20 years * 12 = 240 months
We have to convert the annual rate to a monthly rate and that is done by:
monthly rate = 5.125 / 1,200 = 0.00427083333333333
Monthly pmt = 0.00427083333333333 + [0.00427083333333333 / (1.00427083333333333^240) -1 ] * 420,000
Monthly pmt = 0.00427083333333333 + [0.00427083333333333 / 2.7810190076 -1] * 420,000
Monthly pmt = (0.00427083333333333 +0.0023979718) * 420,000
Monthly pmt = 2,800.90
A calculator to double check is here: https://www.1728.org/calcloan.htm
Step-by-step explanation:
X+y=4 y=3x
x+3x=4
4x=4
divide both sides by 4
x=1
Given that mean=3750 hours and standard deviation is 300:
Then:
<span>a. The probability that a lamp will last for more than 4,000 hours?
P(x>4000)=1-P(x<4000)
but
P(x<4000)=P(z<Z)
where:
z=(x-</span>μ)/σ
z=(4000-3750)/300
z=0.833333
thus
P(x<4000)=P(z<0.8333)=0.7967
thus
P(x>4000)=1-0.7967=0.2033
<span>b.What is the probability that a lamp will last less than 3,000 hours?
P(x<3000)=P(z<Z)
Z=(3000-3750)/300
z=-2.5
thus
P(x<3000)=P(z<-2.5)=0.0062
c. </span><span>.What lifetime should the manufacturer advertise for these lamps in order that only 4% of the lamps will burn out before the advertised lifetime?
the life time will be found as follows:
let the value be x
the value of z corresponding to 0.04 is z=-2.65
thus
using the formula for z-score:
-2.65=(x-3750)/300
solving for x we get:
-750=x-3750
x=-750+3750
x=3000</span>
The answer should be
f=1/5 x^2 + -2/5x
