Final answer:
The mean diameter for the sample of cortex screws is 0 mm, and the standard deviation is 0.021 mm. The probability that 50 randomly selected screws will be within the stated tolerance levels is 50%. The company's claim regarding the diameter of the screws is plausible.
Step-by-step explanation:
a. To find the mean diameter for the sample, we need the sample mean. Since the sample standard deviation is given as s=0.021 mm, we can use the following formula:
Mean = Sample Mean = Population Mean ± (t-value)*(Standard Deviation/Sample Size)
Substituting the given values, we have: Mean = 0 ± (2.048)*(0.021/√28) = 0 ± 0.008 mm
Therefore, the mean diameter for the sample is 0 mm.
To find the standard deviation for the sample, we simply use the given value of s=0.021 mm.
b. To find the probability that 50 randomly selected screws will be within the stated tolerance levels, we need to calculate the z-score. The z-score formula is given by:
Z-score = (X - Mean) / Standard Deviation
Substituting the given values of X=0 mm and Standard Deviation=0.01 mm, we have: Z-score = (0 - 0) / 0.01 = 0
The probability associated with a Z-score of 0 is 0.5, which means there is a 50% chance that 50 randomly selected screws will be within the stated tolerance levels.
Based on the calculated probability, it is plausible that the company's diameter claim is accurate.