Estimate 10/12 - 3/8 using benchmark values. Your equation must show the estimate for each fraction and for the solution.
1 answer:
Answer:
The estimated values of given fraction are 1/2, 1/4 and 1/2 for benchmark values 1/2, 1/4 and 1/8 respectively.
Step-by-step explanation:
The given expression is
Case 1: Let the benchmark value be 1/2.
10/12 > 3/4 so we round it to 1.
1/4 ≤ 3/8 ≤ 3/4 so we round it to 1/2.
Estimating the solution:
1 - 1/2 = 1/2
Case 2: Let the benchmark value be 1/4.
5/8 ≤ 10/12 < 7/8 so we round it to 3/4.
3/8 ≤ 3/8 < 5/8 so we round it to 2/4.
Estimating the solution:
3/4 - 2/4 = 1/4
Case 3: Let the benchmark value be 1/8.
13/16 ≤ 10/12 < 15/16 so we round it to 7/8.
5/16 ≤ 3/8 < 7/16 so we round it to 3/8.
Estimating the solution:
7/8 - 3/8 = 1/2
Therefore the estimated values of given fraction are 1/2, 1/4 and 1/2 for benchmark values 1/2, 1/4 and 1/8 respectively.
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Answer:
a) The 98% confidence interval for the mean weight is between 10.00409 grams and 10.00471 grams
b) 49 measurements are needed.
Step-by-step explanation:
Question a:
We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:
Now, we have to find z in the Ztable as such z has a pvalue of .
That is z with a pvalue of , so Z = 2.327.
Now, find the margin of error M as such
In which is the standard deviation of the population and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 10.0044 - 0.00031 = 10.00409 grams
The upper end of the interval is the sample mean added to M. So it is 10 + 0.00031 = 10.00471 grams
The 98% confidence interval for the mean weight is between 10.00409 grams and 10.00471 grams.
(b) How many measurements must be averaged to get a margin of error of +/- 0.0001 with 98% confidence?
We have to find n for which M = 0.0001. So
Rounding up
49 measurements are needed.