Question

On average, the parts from a supplier have a mean of 97.5 inches and a standard deviation of 6.1 inches. Find the probability that a randomly selected part from this supplier will have a value between 85.3 and 109.7 inches. Use the Empirical Rule of 68%-95%-99.7%.

Answer 1

To find the probability that a randomly selected part from this supplier will have a value between 85.3 and 109.7 inches, we need to standardize the interval and find the corresponding z-scores.

The first step is to calculate the standard score (z-score) for each of the interval boundaries:

z1 = (85.3 - 97.5) / 6.1 = -1.86
z2 = (109.7 - 97.5) / 6.1 = 1.86

The next step is to look up the z-scores in a standard normal distribution table to find the corresponding probabilities:

P(z < -1.86) = 0.0302
P(z < 1.86) = 0.9698

Finally, we subtract the lower probability from the higher one to find the probability that a randomly selected part from the supplier will have a value between 85.3 and 109.7 inches:

P(85.3 < x < 109.7) = 0.9698 - 0.0302 = 0.9396

So, there's a 93.96% probability that a randomly selected part from this supplier will have a value between 85.3 and 109.7 inches