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3 years ago

Round 52961 to one significant figure

Mathematics

1 answer:

Aneli [31]3 years ago

7 0

Answer: 50000

Step-by-step explanation:

Significant figures : The figures in a number which express the value -the magnitude of a quantity to a specific degree of accuracy is known as significant digits.

Rules for significant figures:

Digits from 1 to 9 are always significant and have infinite number of significant figures.

All non-zero numbers are always significant. For example: 654, 6.54 and 65.4 all have three significant figures.

All zero’s between integers are always significant. For example: 5005, 5.005 and 50.05 all have four significant figures.

All zero’s preceding the first integers are never significant. For example: 0.0078 has two significant figures.

All zero’s after the decimal point are always significant. For example: 4.500, 45.00 and 450.0 all have four significant figures.

Thus 52961 when rounded off to one significant figure will be 50000.

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Part A

Answers:
Mean = 5.7
Standard Deviation = 0.046

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The mean is given to us, which was 5.7, so there's no need to do any work there.

To get the standard deviation of the sample distribution, we divide the given standard deviation s = 0.26 by the square root of the sample size n = 32
So, we get s/sqrt(n) = 0.26/sqrt(32) = 0.0459619 which rounds to 0.046

================================================

Part B

The 95% confidence interval is roughly (3.73, 7.67)
The margin of error expression is z*s/sqrt(n)
The interpretation is that if we generated 100 confidence intervals, then roughly 95% of them will have the mean between 3.73 and 7.67

-----------------------

At 95% confidence, the critical value is z = 1.96 approximately

ME = margin of error
ME = z*s/sqrt(n)
ME = 1.96*5.7/sqrt(32)
ME = 1.974949
The margin of error is roughly 1.974949

The lower and upper boundaries (L and U respectively) are:
L = xbar-ME
L = 5.7-1.974949
L = 3.725051
L = 3.73
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U = xbar+ME
U = 5.7+1.974949
U = 7.674949
U = 7.67

================================================

Part C

Confidence interval is (5.99, 6.21)
Margin of Error expression is z*s/sqrt(n)
If we generate 100 intervals, then roughly 95 of them will have the mean between 5.99 and 6.21. We are 95% confident that the mean is between those values.

-----------------------

At 95% confidence, the critical value is z = 1.96 approximately

ME = margin of error
ME = z*s/sqrt(n)
ME = 1.96*0.34/sqrt(34)
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L = lower limit
L = xbar-ME
L = 6.1-0.114286657
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U = upper limit
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U = 6.214286657
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