a random sample of 26 checking accounts at a bank showed an average daily balance of $300 and a standard deviation of $45. the balances of all checking accounts at the bank are normally distributed. develop a 95% confidence interval estimate for the mean of the population.

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08-11-2022
Mathematics

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a random sample of 26 checking accounts at a bank showed an average daily balance of $300 and a standard deviation of $45. the balances of all checking accounts at the bank are normally distributed. develop a 95% confidence interval estimate for the mean of the population.

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jcmacahia7 jcmacahia7 · Answer 1 · 2022-11-10T07:08:47-05:00

The confidence interval estimate for the mean of the population at 95% is [$282.70, $317.30].

Confidence interval is defined as the range of values where a parameter might fall at a given confidence level. It can be calculated using the formula below.

CI = μ ± z x (SD / √n)

where CI = confidence interval

μ = sample mean

z = found by using a z-score table

SD = sample standard deviation

n = sample size

At 95% confidence level, the area in each tail of the standard normal curve is 2.5, and the cumulative area up to the second tail is 97.5.

(100 - 95) / 2 = 2.5

100 - 2.5 = 97.5

Find 0.975 in the z-table to get the value of z.

At p = 0.95, z = 1.96

Plug in the values and solve for the confidence interval.

CI = μ ± z x (SD / √n)

CI = 300 ± 1.96 x (45 / √26)

CI = 300 ± 17.30

CI = [$282.70, $317.30]

Learn more about confidence interval here: brainly.com/question/15905481

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