A paint machine dispenses dye into paint cans to create different shades of paint. The amount of dye dispensed into a can is known to have a normal distribution with a mean of 5 milliliters (ml)
And a standard deviation of 0.4 ml. Answer the following questions based on this information.
What proportion of the paint cans contain less than 5.54 ml of the dye?
A)0.9115
B)0.5885
C)0.9885
D)0.0885

Question

Quizplus · Accepted Answer

To find the proportion of paint cans containing less than 5.54 ml of dye, we calculate the Z-score and then look up the corresponding value in the standard normal distribution table. The Z-score is calculated as $Z = \frac{X - \mu}{\sigma}$, where $X$ is the value of interest (5.54 ml), $\mu$ is the mean (5 ml), and $\sigma$ is the standard deviation (0.4 ml). Plugging in the values, we get $Z = \frac{5.54 - 5}{0.4} = 1.35$. Looking up the Z-score of 1.35 in the standard normal distribution table gives us a value of approximately 0.9115, indicating that about 91.15% of the paint cans contain less than 5.54 ml of dye.

A Paint Machine Dispenses Dye into Paint Cans to Create