Question

In a production, the length of the box follows a normal distribution with a mean of 2.83 and the population standard deviation is 1.76m. Determine the percentage of the pen with a length more than 4.33m, between 1.54 and 5.67m, less than 0.95m, and between 1.73 and 2.12m.

Answer 1

To determine the percentage of pens with certain lengths, we can find the corresponding z-scores and use the standard normal distribution table.

Step-by-step explanation:

To determine the percentage of pens with a length more than 4.33m, we can calculate the z-score for 4.33 using the formula:

z = (x - μ) / σ.

Substituting the values, z = (4.33 - 2.83) / 1.76 = 0.8523.

Using the standard normal distribution table, we can find the percentage of the area to the right of 0.8523, which is approximately 0.1975 or 19.75%.

To find the percentage of pens with a length between 1.54m and 5.67m, we can calculate the z-scores for both values and find the area between them using the standard normal distribution table.

To find the percentage of pens with a length less than 0.95m, we can calculate the z-score for 0.95 and find the area to the left of the z-score.

To find the percentage of pens with a length between 1.73m and 2.12m, we can calculate the z-scores for both values and find the area between them using the standard normal distribution table.