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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?

Respuesta :

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:

[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]

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

[tex]P( x < 5.54) = P( z < \displaystyle\frac{5.54 - 5}{0.4}) = P(z < 1.35)[/tex]

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

[tex]P(x < 5.54) =0.9115 = 91.15\%[/tex]

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

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

Calculation of the proportion:

Since the mean of 5 milliliters (ml) and a standard deviation of 0.4 ml.

So, for determining the proportion first determine the z-score

So, z score should be

P(x<5.54)  = [tex]P(z < (5.54-5)\div 0.4) = P(z < 1.35)[/tex]

Now

P(x<5.54) = 0.9115

Therefore, The proportion of the paint cans contain less than 5.54 ml of the dye is 0.9115.

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