Answer:
1.5 hours
Step-by-step explanation:
1/2 + 1/2 + 1/2 =1.5
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>
Simple just do normal simple algebra:)
The expression will be d. 9-7i
Answer:
The probability that the proportion of books checked out in a sample of 412 books would differ from the population proportion by less than 4% is P=0.9255.
Step-by-step explanation:
The population's proportion is 
If we take a sample of 412 books (n=412), we have a standard deviation of the sampling distribution of:
We have to calculate the probabilty that the sample proportion will be between 0.25 and 0.33.
