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>
This is the concept of differential equations, given that
dp/dt=rp
then:
dp/p=rdt
thus:
ln p=rt+C
p=e^(rt+C)
P=Ke^(rt)
when t=210 days=7 months, p=2k
2k=k×e^(7r)
2=e^(7r)
ln2=7r
r=ln(2)/7
r=0.0990
The perimeter of the polygon that circumscribes the circle is 78 cm
<h3>What is an
equation?</h3>
An equation is an expression that shows the relationship between two or more variables and numbers.
The circle tangent theorem states that tangents which meet at the same point are equal in length. Hence:
The missing lengths are 8, 6, 9 and 16.
Perimeter of the polygon = 2(8) + 2(6) + 2(9) + 2(16) = 78 cm
The perimeter of the polygon that circumscribes the circle is 78 cm
Find out more on equation at: brainly.com/question/2972832
#SPJ1
Answers A mark me brainliest
Answer:
The mean is 8.
Step-by-step explanation:
The mean is the sum of a set of numbers divided by the number of numbers in a set. In this case, you add up all the numbers to get 56, and divide by 7 to get 8.
