For a sample of $n=70$, the probability of a sample mean being greater than 213 if $\mu=212$ and $\sigma=5.9$ is 0.0781 .
Round to four decimal places as needed.)
Would the given sample mean be considered unusual?
The sample mean be considered unusual because it within the range of a usual event, namely within of the mean of the sample mear
Answer
\(\boxed{\text{The sample mean of 213 would not be considered unusual.}}\)
Step 1 ：The problem is asking whether a sample mean of 213 is considered unusual for a sample of size 70, given that the population mean is 212 and the standard deviation is 5.9. The probability of getting a sample mean greater than 213 is given as 0.0781.
Step 2 ：In statistics, an event is often considered unusual if its probability is less than or equal to 0.05. Therefore, we need to compare the given probability (0.0781) with 0.05 to determine whether the sample mean is unusual.
Step 3 ：The probability of getting a sample mean greater than 213 is 0.0781, which is greater than the threshold of 0.05.
Step 4 ：Therefore, the sample mean of 213 would not be considered unusual.
Step 5 ：\(\boxed{\text{The sample mean of 213 would not be considered unusual.}}\)
