Final answer:
To find the percentage of sheets suitable for the new car model, we use the properties of a normal distribution. The required thickness range is 0.495 to 0.525 inches. Using z-scores and a standard normal distribution table, we find that approximately 30.94% of the sheets will be suitable.
Step-by-step explanation:
To find the percentage of sheets made by the steel mill that will be suitable for the new car model, we can use the properties of a normal distribution. The average thickness of the sheets produced by the mill is 0.517 inches, with a standard deviation of 0.037 inches. The new car model requires sheets between 0.495 and 0.525 inches thick.
First, we calculate the z-scores for the lower and upper limits of the required thickness range:
Z(lower) = (0.495 - 0.517) / 0.037 = -0.595
Z(upper) = (0.525 - 0.517) / 0.037 = 0.216
Next, we use a standard normal distribution table or a calculator to find the percentage of values within this range. From the table, we find that the area to the left of Z(lower) is approximately 0.2764 and the area to the left of Z(upper) is approximately 0.5858.
To find the percentage within the required thickness range, we subtract the area to the left of Z(lower) from the area to the left of Z(upper):
Percentage = 0.5858 - 0.2764 = 0.3094 = 30.94%
Therefore, approximately 30.94% of the sheets made by the steel mill will be suitable for the new car model.