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madreJ [45]
3 years ago
8

Guest ages at a ski mountain resort typically have a right-skewed distribution. Assume the standard deviation (σ) of age is 14.5

years. From a random sample of 40 guests the sample mean is 36.4 years. Calculate a 99 percent confidence interval for µ, the true mean age of guests.
Mathematics
1 answer:
ValentinkaMS [17]3 years ago
7 0

Answer: (30.49 years, 42.31 years)

Step-by-step explanation:

The formula to find the confidence interval is given by :-

\overline{x}\pm z^*\dfrac{\sigma}{\sqrt{n}}.

, where \overline{x} = Sample mean

z* = Critical value.

\sigma = Population standard deviation.

n= Sample size.

As per given , we have

\overline{x}=36.4

\sigma=14.5

n= 40

We know that the critical value for 99% confidence interval : z* = 2.576 (By z-table)

A 99 percent confidence interval for µ, the true mean age of guests will be :

36.4\pm (2.576)\dfrac{14.5}{\sqrt{40}}\\\\ 36.4\pm (2.576)2.29265130362\\\\=36.4\pm5.90586975813\\\\\approx36.4\pm5.91\\\\=(36.4-5.91,\ 36.4+5.91)\\\\=(30.49,\ 42.31)

∴ a 99 percent confidence interval for µ, the true mean age of guests  = (30.49 years, 42.31 years)

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