Determine if the mean weight of the sample justifies shutting down the machinery:
Current Attempt in Progress
The weight of a USB flash drive is 30 grams and is normally distributed. Periodically, quality control inspectors at Dallas Flash Drives randomly select a sample of 17 USB flash drives. If the mean weight of the USB flash drives is too heavy or too light the machinery is shut down for adjustment; otherwise, the production process continues. The last sample showed a mean and standard deviation of 31.9 and 1.8 grams, respectively. Using $\mathrm{a}=0.10$, the appropriate decision is to
do nothing
reject the null hypothesis and shut down the process
fail to reject the null hypothesis and do not shut down the process
reject the null hypothesis and do not shut down the process
fail to reject the null hypothesis and shut down the process

Step 1 ：Given values are: sample mean = 31.9, population mean = 30, standard deviation = 1.8, sample size = 17, and significance level = 0.10.

Step 2 ：Calculate the z-score using the formula \((\text{sample mean} - \text{population mean}) / (\text{standard deviation} / \sqrt{\text{sample size}})\).

Step 3 ：Substitute the given values into the formula to get the z-score: \(z = (31.9 - 30) / (1.8 / \sqrt{17}) = 4.352167049263083\).

Step 4 ：The critical value for a two-tailed test at a significance level of 0.10 is 1.645.

Step 5 ：Compare the z-score with the critical value. If the z-score is greater than the critical value, reject the null hypothesis and shut down the process. If the z-score is less than the critical value, fail to reject the null hypothesis and do not shut down the process.

Step 6 ：Since the z-score (4.352167049263083) is greater than the critical value (1.645), the decision is to reject the null hypothesis and shut down the process.

Step 7 ：Final Answer: \(\boxed{\text{Reject the null hypothesis and shut down the process}}\)