A technician plans to test a certain type of resin developed in a laboratory to determine the nature of the time it takes before bonding takes place. it is known that the time to bonding is normally distributed with a mean of 4.5 hours and a standard deviation of 1.5 hours. it will be considered an undesirable product if the bonding time is either less than 2 hours or more than 6 hours

In this item, we are to determine the number of the resin in terms of percentage that has a bonding time of either less than 2 hours or more than 6 hours.

To do so, we use the concept of z-score. Z-score is calculated through the equation,

z-score = (x - m) / s

where x is the data, m is the mean/average, and s is the standard deviation. Substituting the known values,

Less than 2 hours:

z-score = (2 - 4.5) / 1.5 = - 5/3

This translates to the percentile of 4.78%.

More than 6 hours:

z-score = (6 - 4.5) / 1.5 = 1

This translates to percentile of 84.13%. The percentage of more than 6 hours is equal to 100% - 84.13% which is equal to 15.87%.

The total percentage is equal to 4.78% and 15.87% which is equal to 24.65%.