Question

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?

Answer 1

Answer:

0.9115 is the proportion of paint cans that contain less than 5.54 ml of the dye.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 5 ml

Standard Deviation, σ = 0.4 ml

We are given that the distribution of amount of dye dispensed is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

P(paint cans contain less than 5.54 ml of the dye)

$P( x < 5.54) = P( z < \displaystyle\frac{5.54 - 5}{0.4}) = P(z < 1.35)$

Calculation the value from standard normal z table, we have,  

$P(x < 5.54) =0.9115 = 91.15\%$

0.9115 is the proportion of paint cans that contain less than 5.54 ml of the dye.