What is the probability that the inside diameter of a randomly chosen washer is less than 0.515 inches?
What is the probability that the inside diameter of random samples of 35 washers is greater than 0.492 inches?
Final answer:
The probability that the inside diameter of a randomly chosen washer is less than 0.515 inches is approximately 0.9953.
The probability that the inside diameter of random samples of 35 washers is greater than 0.492 inches is approximately 0.
Probability Calculation for Washer Diameter
Part a: Probability for Diameter < 0.515 inches
To find the probability that the inside diameter of a randomly chosen washer is less than 0.515 inches, we can use the properties of the normal distribution. First, we calculate the z-score for 0.515 inches, which is 2.6. Using a standard normal distribution table, we find the corresponding probability to be approximately 0.9953. Thus, the probability that the inside diameter of a randomly chosen washer is less than 0.515 inches is approximately 0.9953.
Part b: Probability for Random Samples of 35 Washers > 0.492 inches
To find the probability that the inside diameter of random samples of 35 washers is greater than 0.492 inches, we need to use the standard error of the mean. The standard error is calculated to be approximately 0.000843. Next, we calculate the z-score for 0.492 inches, which is approximately -11.87. Using a standard normal distribution table, we find that the probability corresponding to a z-score of -11.87 is approximately 0. Therefore, the probability that the inside diameter of random samples of 35 washers is greater than 0.492 inches is approximately 0.