michaelborne04pec1tt
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Ill Give Brainlyiest The height of pyramids in Egypt is normally distributed. A sample of 125 pyramids had a mean height of 460.7 ft and a standard deviation of 4.1 feet. With 80% confidence, what is the maximum error of estimate for the actual population mean for the height of Egyptian pyramids?


37.04%

47.01%

4.21%

94.43%

Sagot :

Using the t-distribution, as we have the standard deviation for the sample, it is found that the the maximum error of estimate for the actual population mean for the height of Egyptian pyramids is of 47.01%.

What is a t-distribution confidence interval?

The confidence interval is:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which:

  • [tex]\overline{x}[/tex] is the sample mean.
  • t is the critical value.
  • n is the sample size.
  • s is the standard deviation for the sample

The margin of error is:

[tex]M = t\frac{s}{\sqrt{n}}[/tex]

The critical value, using a t-distribution calculator, for a two-tailed 80% confidence interval, with 125 - 1 = 124 df, is t = 1.2884.

The other parameters are: [tex]\mu = 460.7, s = 4.1, n = 125[/tex].

Hence, the margin of error is of:

[tex]M = t\frac{s}{\sqrt{n}}[/tex]

[tex]M = 1.2884\frac{4.1}{\sqrt{125}}[/tex]

[tex]M = 0.47[/tex]

Hence, the maximum error of estimate for the actual population mean for the height of Egyptian pyramids is of 47.01%.

More can be learned about the t-distribution at https://brainly.com/question/16162795

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