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Question:
The lifetime (in hours) of a 60-watt light bulb is a random variable that has a Normal distribution with σ = 30 hours. A random sample of 25 bulbs put on test produced a sample mean lifetime of = 1038 hours.
If in the study of the lifetime of 60-watt light bulbs it was desired to have a margin of error no larger than 6 hours with 99% confidence, how many randomly selected 60-watt light bulbs should be tested to achieve this result?
Given Information:
standard deviation = σ = 30 hours
confidence level = 99%
Margin of error = 6 hours
Required Information:
sample size = n = ?
Answer:
sample size = n ≈ 165
Step-by-step explanation:
We know that margin of error is given by
Margin of error = z*(σ/√n)
Where z is the corresponding confidence level score, σ is the standard deviation and n is the sample size
√n = z*σ/Margin of error
squaring both sides
n = (z*σ/Margin of error)²
For 99% confidence level the z-score is 2.576
n = (2.576*30/6)²
n = 164.73
since number of bulbs cannot be in fraction so rounding off yields
n ≈ 165
Therefore, a sample size of 165 bulbs is needed to ensure a margin of error not greater than 6 hours.
Answer:
4 ft, 2 in
Step-by-step explanation:
2 ft, 8 in plus 1 ft, 6 in = 3 ft, 14 in
there are 12 inches in a foot
3 ft, 14 in equals 4 ft, 2 in
The required Comparison of the inequalities are
- The |x – 1| + 1 > 15 represents the value of x lies between 13<x<15.
The range of values encompassing the region's junction is (-13, 15).
- If x is more than or equal to 15, then x-11+1>15 indicates the value of x is greater than or equal to 13. None of the regions in the intersection are empty.
<h3>What is inequality?</h3>
When comparing two numbers, an inequality indicates whether one is less than, larger than, or not equal to the other.
We take into account the various variables of the inequality
|x – 1| + 1 > 15
Therefore
|-x-1|+1-1<15-1
|-x-1|-1 <14
13<x<15
The required region lies between the inequality -13 <x< 15.
Simplify the inequality Ix-11+1 > 15 we get,
|x-1|+1 > 15
|x+1| +1-1 >15-1
|x-1| > 14
x> 15
x<-13
- If x has a value between -13 and x + 15, then the expression "|x-1|+1+115" is true. The range "(-13, 15)" contains the intersection of the region.
- If "|x-1|+1>15" then either "x >15" or "x-13" applies to the value of x. This region's intersection is unoccupied.
Read more about inequalities
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Answer:
f(6) = 3(6) - 9
Step-by-step explanation:
y = 3(6) - 9
y = 18 - 9
y / f(x) = 9
Answer:
6
Step-by-step explanation:
the middle number of the given list
