a simple random sample of 90 is drawn from a normally distributed population, and the mean is found to be…

a simple random sample of 90 is drawn from a normally distributed population, and the mean is found to be 138, with a standard deviation of 34. what is the 90% confidence interval for the population mean? use the table below to help you answer the question.\n| confidence level | 90% | 95% | 99% |\n| ---- | ---- | ---- | ---- |\n| $z^{*}$-score | 1.645 | 1.96 | 2.58 |\nremember, the margin of error, $me$, can be determined using the formula $me = \\frac{z^{*}s}{\\sqrt{n}}$.\n128.75 to 147.25\n130.98 to 145.02\n132.10 to 143.90\n137.38 to 138.62

a simple random sample of 90 is drawn from a normally distributed population, and the mean is found to be 138, with a standard deviation of 34. what is the 90% confidence interval for the population mean? use the table below to help you answer the question.\n| confidence level | 90% | 95% | 99% |\n| ---- | ---- | ---- | ---- |\n| $z^{*}$-score | 1.645 | 1.96 | 2.58 |\nremember, the margin of error, $me$, can be determined using the formula $me = \\frac{z^{*}s}{\\sqrt{n}}$.\n128.75 to 147.25\n130.98 to 145.02\n132.10 to 143.90\n137.38 to 138.62

Answer

Explanation:

Step1: Identify given values

$n = 90$, $\bar{x}=138$, $s = 34$, $z^*=1.645$ (for 90% confidence level)

Step2: Calculate margin of error

$ME=\frac{z^*\cdot s}{\sqrt{n}}=\frac{1.645\times34}{\sqrt{90}}$ $=\frac{1.645\times34}{9.4868}\approx\frac{55.93}{9.4868}\approx5.9$

Step3: Calculate confidence - interval lower bound

Lower bound $=\bar{x}-ME=138 - 5.9=132.1$

Step4: Calculate confidence - interval upper bound

Upper bound $=\bar{x}+ME=138 + 5.9=143.9$

Answer:

132.10 to 143.90