Question

question 20 (1 point) saved

solve the problem.

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. find the dye amount that represents the 10th percentile of the distribution.

4.464 ml
4.836 ml
4.964 ml
4.487 ml
4.936 ml

once you are done, submit this quiz by clicking \submit quiz\ button (some times twice) and \done\ button.

Explanation:

Identify the given parameters

Using the Normal Distribution Properties knowledge point

$$
LATEXBLOCK0
$$

Find the standard normal Z-score

Using the Normal Distribution Percentiles knowledge point

$$
LATEXBLOCK1
$$

Calculate the corresponding dye amount

Using the Z-score Calculation knowledge point

$$
LATEXBLOCK2
$$

Match with the closest option

Using the Normal Distribution Properties knowledge point

$$ x \approx 4.487\text{ ml} $$

Answer:

• (A) 4.464 ml
• (B) 4.836 ml
• (C) 4.964 ml
• (D) 4.487 ml (Correct answer)
• (E) 4.936 ml