The question is incomplete! Complete question along with answer and step by step explanation is provided below.
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:
Simplify 4/ (square root of 5) 4 √5 4 5 Multiply 4 √5 4 5 by √5 √5 5 5. 4 √5 ⋅ √5 √5 4 5 ⋅ 5 5
Step-by-step explanation:
The probability would be 0.9738.
We first find the z-score for each end of this interval:
z = (x-μ)/(σ/√n) = (100-110)/(18/√49) = -10/(18/7) = -3.89
z = (x-μ)/(σ/√n) = (115-110)/(18/√49) = 5/(18/7) = 1.94
Using a z-table (http://www.z-table.com) we see that the probability that a score is less than the first z-score is 0. The probability under the curve to the left of, less than, the second z-score is 0.9738. Subtracting these we find the area between them:
0.9738 - 0 = 0.9738.
Answer:
Step 1: Given
Step 2: Add 6 on both sides
Step 3: Multiply 7 on both sides
Step 4: Divide by 4 on both sides
Answer:
You begin with 1 bacteria, and after 1 hour it has tripled so you now have 1 x 3=3.
Next hour, it triples again so you now have 1 x 3 x 3=9
You can see the pattern shows that the number of bacteria is multiplying every hour by a factor of 3. An exponent denotes how many times we are multiplying a number by itself, for example: 34 means we are multiplying the number 3 a total of 4 times (3 x 3 x 3 x 3).
Therefore the question is requiring us to triple the number of bacteria every hour for 24 hours, which means we are multiplying by 3 a total of 24 times. This gives us:
n x 324 where n is the number of bacteria you begin with.
Since you begin with 1 bacteria, the solution is 1 x 3 to the power 24 and u will get ur answer
