Question

The time required to assemble an electronic component is normally distributed with a mean and a standard deviation of 20 minutes and 14 minutes, respectively.It is unusual for the assembly time to be above 38 minutes or below 2 minutes. What proportion of assembly times fall in these unusual categories?

Answer 1

To find the proportion of assembly times that fall above 38 minutes or below 2 minutes, calculate the z-scores for these two values and use a z-table or calculator to find the proportions under the curve.

Step-by-step explanation:

To find the proportion of assembly times that fall above 38 minutes or below 2 minutes, we need to calculate the z-scores for these two values. The z-score formula is: Z = (X - Mean) / Standard Deviation.

For X = 38 minutes: Z = (38 - 20) / 14 = 1.29. For X = 2 minutes: Z = (2 - 20) / 14 = -1.29.

Next, we can use a z-table or a calculator to find the proportion under the curve for these z-scores.

Look up the z-scores in the table or calculate using a calculator, and subtract the proportions from 0.5 to get the proportions above 38 minutes and below 2 minutes.

In this case, the proportion above 38 minutes is 1 - 0.9015 = 0.0985, and the proportion below 2 minutes is 0.5 - 0.0985 = 0.4015.