Question

for a sample of 110 transformers built for heavy industry, the mean and standard deviation of the number of swells per week were 151 and 15, respectively. consider a transformer that has 285 swells and 174 swells in a week. complete parts a and b below. a. would you consider 174 swells per week unusual, statistically? explain. select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. yes. the z - score is (round to two decimal places as needed.), meaning that this is an outlier and almost every other transformer has fewer swells. b. no. the z - score is (round to two decimal places as needed.), meaning that the number of swells is not unusual and is not an outlier. c. yes. the z - score is (round to two decimal places as needed.), meaning that this is an outlier and almost every other transformer has more swells. d. no. the z - score is (round to two decimal places as needed.), meaning that less than approximately 68% of transformers have a number of swells closer to the mean.

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: Identify values for the problem

We are given that for the number of swells, $\mu = 151$, $\sigma = 15$, and $x = 174$.

Step3: Calculate the z - score

Substitute the values into the formula: $z=\frac{174 - 151}{15}=\frac{23}{15}\approx1.53$.

Step4: Determine if it's unusual

A z - score between - 2 and 2 is considered not unusual. Since $|1.53|\lt2$, the value of 174 swells is not unusual.

Answer:

B. No. The z - score is 1.53, meaning that the number of swells is not unusual and is not an outlier.