Final answer:
The calculating z-scores with a TI-calculator to determine which manufacturing machine is more likely to produce a bolt of a specific length. The machine with a z-score closest to zero for a 43.97mm bolt would be considered more consistent in producing that length. Required data and functions on the calculator are necessary to perform the actual calculations.
Step-by-step explanation:
The requires an analysis of sample data to determine the likelihood of a manufacturing plant's machinery producing a bolt of a specific length. To calculate the z-score for a 43.97mm bolt produced by machines A and B, you would first find the mean (average) length and the standard deviation of the lengths for the bolts produced by each machine. These statistical measurements allow us to understand the dispersion of the data and how far a single measurement is from the mean.
To proceed with a TI-83, TI-83 Plus, or TI-84 calculator, one would input the lengths for the bolts from each machine, utilize the built-in functions to calculate the mean and standard deviation, then apply the formula for the z-score, which is (x - μ) / σ, where x is the bolt length you're investigating (43.97mm), μ is the mean, and σ is the standard deviation. The machine with the z-score closest to zero would be more likely to produce bolts of the length of 43.97mm consistently.