Question

1. problem solving to estimate the margin of error when the standard deviation of a sample is known, you can use the formula margin of error = ±\\(\frac{2\sigma}{\sqrt{n}}\\) where \\(\sigma\\) is the standard deviation of the sample data and \\(n\\) is the sample size. to estimate the number of times cell phone users check their phone each day, a national polling company surveys a random sample of 2000 cell phone users. the sample has a mean of 52 checks per day and a standard deviation of 11 checks per day. a. find the margin of error. round your answer to the nearest thousandth. about ± 1 correct answers: 1 0.492 interpret the margin of error. 0 / 10000 word limit b. give an interval that is likely to contain the actual population mean. round your answers to the nearest thousandth. the interval is between 1 and 2 correct answers:

Explanation:

Step1: Identify values of $\sigma$ and $n$

$\sigma = 11$, $n=2000$

Step2: Substitute values into formula

Margin of error $=\pm\frac{2\sigma}{\sqrt{n}}=\pm\frac{2\times11}{\sqrt{2000}}$

Step3: Calculate the value

$\sqrt{2000}\approx44.7214$, $2\times11 = 22$, $\frac{22}{44.7214}\approx0.492$

Answer:

a. about $\pm0.492$
b. The interval is between $52 - 0.492=51.508$ and $52 + 0.492 = 52.492$

1. $51.508$
2. $52.492$