Question

The drying time of acrylic paint is normally distributed with a mean of 2 hours 36 minutes and a standard deviation of 24 minutes. Find the probability that the drying time will be between 2 hours and 3 hours.

Answer 1

To find the probability that the drying time of acrylic paint will be between 2 hours and 3 hours, convert the hours into minutes, use the z-score formula, and find the difference between the probabilities.

Step-by-step explanation:

To find the probability that the drying time of acrylic paint will be between 2 hours and 3 hours, we need to convert the hours into minutes and then use the z-score formula.

First, convert 2 hours to minutes: 2 hours x 60 minutes = 120 minutes.

Next, convert 3 hours to minutes: 3 hours x 60 minutes = 180 minutes.

Next, subtract the mean from each value: 120 minutes - 156 minutes (mean in minutes) = -36 minutes and 180 minutes - 156 minutes (mean in minutes) = 24 minutes.

Finally, use the z-score formula to find the probability:

z = (x - mean) / standard deviation

For -36 minutes, the z-score is -36 / 24 = -1.5.

For 24 minutes, the z-score is 24 / 24 = 1.

You can use a standard normal distribution table or a calculator to find the probabilities corresponding to these z-scores. The probability that the drying time will be between 2 hours and 3 hours is the difference between these two probabilities.