The heights would be outside the 95% confidence interval will be 84.6 feet. Then the correct option is B.
If the sample size is given to be n < 30, then for finding the confidence interval for mean of population from this small sample, we use t-statistic.
Let the sample mean given as μ and
The sample standard deviation σ, and
The sample size = n, and
Suppose that a travel bureau claims that the trees in a forest are 85 feet tall on average, with a standard deviation of 2 feet.
If you took a sample of 64 trees.
Then the heights would be outside the 95% confidence interval will be
For 95% confidence interval, we have z = 1.645
⇒ μ ± z (σ/√n)
⇒ 85 ± 1.645 (2/√64)
For negative sign, we have
⇒ 84.588
⇒ 84.6 feet
For negative sign, we have
⇒ 85.41
⇒ 85.4 feet
Then the correct option is B.
Learn more about confidence interval of population for small sample here:
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