Question

Suppose that a sample of size 100 is to be drawn from a population with standard deviation 10 . a. What is the probability that the sample mean will be within 1 of the value of $\mu$ ? b. For this example $(n=100, \sigma=10)$, complete each of the following statements by computing the appropriate value: i. Approximately $95 \%$ of the time, $\bar{x}$ will be within of $\mu$. ii. Approximately $0.3 \%$ of the time, $\bar{x}$ will be farther than $\quad$ from $\mu$.

          Suppose that a sample of size 100 is to be drawn from a population with standard deviation 10 .
a. What is the probability that the sample mean will be within 1 of the value of $\mu$ ?
b. For this example $(n=100, \sigma=10)$, complete each of the following statements by computing the appropriate value:
i. Approximately $95 \%$ of the time, $\bar{x}$ will be within of $\mu$.
ii. Approximately $0.3 \%$ of the time, $\bar{x}$ will be farther than $\quad$ from $\mu$.

Added by Jonathan K.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Qudsiya Anis

03/03/2022

Step 1

The standard deviation of the sample mean, also known as the standard error, is given by $\sigma/\sqrt{n}$, where $\sigma$ is the population standard deviation and $n$ is the sample size. In this case, the standard error is $10/\sqrt{100} = 1$. The question asks Show more…

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Suppose that a sample of size 100 is to be drawn from a population with standard deviation 10 . a. What is the probability that the sample mean will be within 1 of the value of $\mu$ ? b. For this example $(n=100, \sigma=10)$, complete each of the following statements by computing the appropriate value: i. Approximately $95 \%$ of the time, $\bar{x}$ will be within of $\mu$. ii. Approximately $0.3 \%$ of the time, $\bar{x}$ will be farther than $\quad$ from $\mu$.