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>
Answer:
The answer is C the 2 rectangles
Let's solve your inequality step-by-step.<span><span><span>−1</span>+<span>4y</span></span><31</span>Step 1: Simplify both sides of the inequality.<span><span><span>4y</span>−1</span><31</span>Step 2: Add 1 to both sides.<span><span><span><span>4y</span>−1</span>+1</span><<span>31+1</span></span><span><span>4y</span><32</span>Step 3: Divide both sides by 4.<span><span><span>4y</span>4</span><<span>324</span></span><span>y<<span>8</span></span>
