Question

4. The length of an injected-molded plastic case that holds tape is normally distributed with a mean length of 90.2 millimeters and a standard deviation of 0.1 millimeters. a. What is the probability that a part is longer than 90.3 millimeters or shorter than 89.7 millimeters

Answer 1

To find the probability that a part is longer than 90.3 millimeters or shorter than 89.7 millimeters, calculate the cumulative probability for each scenario and subtract them from 1. The resulting probability is approximately 0.8413.

Step-by-step explanation:

To find the probability that a part is longer than 90.3 millimeters or shorter than 89.7 millimeters, we need to calculate the cumulative probability for each scenario and then subtract them from 1.

Step 1: Calculate the z-scores for both values using the formula:

z = (x - mean) / standard deviation

For 90.3 millimeters:

z = (90.3 - 90.2) / 0.1 = 1

For 89.7 millimeters:

z = (89.7 - 90.2) / 0.1 = -5

Step 2: Use a standard normal distribution table or a calculator to find the cumulative probability for each z-score.

For a z-score of 1, the cumulative probability is approximately 0.8413.

For a z-score of -5, the cumulative probability is approximately 0.0000003.

Step 3: Subtract the cumulative probability for the shorter length from 1 and add the cumulative probability for the longer length.

Probability = (1 - 0.0000003) + 0.8413 = 0.8413

Therefore, the probability that a part is longer than 90.3 millimeters or shorter than 89.7 millimeters is approximately 0.8413.

Answer 2

Step-by-step explanation:

The length of an injected-molded plastic case that holds tape is normally distributed with a mean length of 90.2 millimeters and a standard deviation of 0.1 millimeters. a. What is the probability that a part is longer than 90.3 millimeters or shorter than 89.7 millimeters