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A researcher for a travel company is looking into the prices people are willing to pay for airplane tickets. The company has communicated that the overall population mean is $265 with a standard deviation of $40. 93. The researcher has a sample of 130 ticket purchases from one location. By the central limit theorem, which interval can the researcher be 95% certain that the sample mean will fall within?

Respuesta :

The interval can the researcher be 95% certain that the sample mean will fall within $258.13 and $271.87.

Central limit theorem states that the distribution of a sample variable approximates a normal distribution as the sample size become larger, assuming that all samples are identical in size and regardless of the population's actual distribution shape.

We know the formula for Central limit theorem is,

Sample standard deviation = (standard deviation) / [tex]\sqrt{n} \\[/tex] = σ/[tex]\sqrt{n}[/tex]

Here population mean (μ) = $265

standard deviation = $40.93

sample size = 130

for confidence level 95% the formula is,

CI = μ ± 1.96 * (σ/[tex]\sqrt{n}[/tex])

⇒ CI = 265 ± 1.96 * (40/[tex]\sqrt{130}[/tex])

        = 265 ± 1.96 * 3.51

        = 265 ± 6.87

⇒ 265 + 6.87 =271.87  and 265 - 6.87 = 258.13

Therefore sample mean will fall within $258.13 and $271.87.

To know more about confidence interval here

https://brainly.com/question/20193183

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