a simple random sample of 60 is drawn from a normally distributed population, and the mean is found to be…

a simple random sample of 60 is drawn from a normally distributed population, and the mean is found to be 28, with a standard deviation of 5. which of the following values is within the 95% confidence interval (z - score = 1.96) for the population mean?\nremember, the margin of error, me, can be determined using the formula $me = \\frac{z\\cdot s}{\\sqrt{n}}$.\no the value of 26, because its not greater than 26.7 and less than 29.3.\no the value of 27, because its greater than 26.7 and less than 29.3.\no the value of 32, because its greater than 23 and less than 33.\no the value of 34, because its not greater than 23 and less than 33.

a simple random sample of 60 is drawn from a normally distributed population, and the mean is found to be 28, with a standard deviation of 5. which of the following values is within the 95% confidence interval (z - score = 1.96) for the population mean?\nremember, the margin of error, me, can be determined using the formula $me = \\frac{z\\cdot s}{\\sqrt{n}}$.\no the value of 26, because its not greater than 26.7 and less than 29.3.\no the value of 27, because its greater than 26.7 and less than 29.3.\no the value of 32, because its greater than 23 and less than 33.\no the value of 34, because its not greater than 23 and less than 33.

Answer

Explanation:

Step1: Identify the given values

$n = 60$, $\bar{x}=28$, $s = 5$, $z = 1.96$

Step2: Calculate the margin of error

$ME=\frac{z\cdot s}{\sqrt{n}}=\frac{1.96\times5}{\sqrt{60}}\approx\frac{9.8}{7.746}\approx1.278$

Step3: Calculate the confidence - interval

The lower limit is $\bar{x}-ME=28 - 1.278=26.722$ The upper limit is $\bar{x}+ME=28 + 1.278=29.278\approx29.3$

Answer:

The value of 27, because it's greater than 26.7 and less than 29.3.