for a sample of 117 transformers built for heavy industry, the mean and standard deviation of the number of…

for a sample of 117 transformers built for heavy industry, the mean and standard deviation of the number of swells per week were 174 and 23, respectively. consider a transformer that has 277 sags and 208 swells in a week. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. no. the z - score is , meaning that less than approximately 68% of transformers have a number of sags closer to the mean. (round to two decimal places as needed.) b. yes. the z - score is , meaning that this is an outlier and almost every other transformer has fewer sags. (round to two decimal places as needed.) c. yes. the z - score is , meaning that this is an outlier and almost every other transformer has more sags. (round to two decimal places as needed.) d. no. the z - score is , meaning that the number of sags is not unusual and is not an outlier. (round to two decimal places as needed.) e. this cannot be determined, since the iqr is not provided and cannot be found from the provided information.

for a sample of 117 transformers built for heavy industry, the mean and standard deviation of the number of swells per week were 174 and 23, respectively. consider a transformer that has 277 sags and 208 swells in a week. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. no. the z - score is , meaning that less than approximately 68% of transformers have a number of sags closer to the mean. (round to two decimal places as needed.) b. yes. the z - score is , meaning that this is an outlier and almost every other transformer has fewer sags. (round to two decimal places as needed.) c. yes. the z - score is , meaning that this is an outlier and almost every other transformer has more sags. (round to two decimal places as needed.) d. no. the z - score is , meaning that the number of sags is not unusual and is not an outlier. (round to two decimal places as needed.) e. this cannot be determined, since the iqr is not provided and cannot be found from the provided information.

Answer

Explanation:

Step1: Recall z - score formula

The z - score formula is $z=\frac{x - \mu}{\sigma}$, where $x$ is the data - point, $\mu$ is the mean, and $\sigma$ is the standard deviation.

Step2: Calculate z - score for the first case

For the first transformer with $x = 277$ sags, $\mu = 174$ sags, and $\sigma = 23$ sags. $z_1=\frac{277 - 174}{23}=\frac{103}{23}\approx4.48$

Step3: Analyze the z - score

A z - score with a magnitude greater than 3 is considered an outlier. Since $z_1\approx4.48>3$, this is an outlier.

Step4: Calculate z - score for the second case

For the second transformer with $x = 208$ sags, $\mu = 370$ sags, and $\sigma = 26$ sags. $z_2=\frac{208 - 370}{26}=\frac{- 162}{26}\approx - 6.23$

Step5: Analyze the z - score

Since $|z_2|\approx6.23>3$, this is also an outlier.

Answer:

B. Yes. The z - score is [calculated value], meaning that this is an outlier and almost every other transformer has fewer sags. (Round to two decimal places as needed.)