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the diameters of pencils produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. What is the probability that the diameter of a randomly selected pencil will be less than 0.285​ inches? Round your answer to four decimal places.

Respuesta :

Answer: P(x < 0.285) = 0.0668

Step-by-step explanation:

Since the diameters of pencils produced by the machine are normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = diameters of pencils produced .

µ = mean diameter

σ = standard deviation

From the information given,

µ = 0.30 inches

σ = 0.01 inches

The probability that the diameter of a randomly selected pencil will be less than 0.285​ inches is expressed as

P(x < 0.285)

For x = 0.285

z = (0.285 - 0.30)/0.01 = - 1.5

Looking at the normal distribution table, the probability corresponding to the z score is 0.0668

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