Question

Fast Auto Service provides a lubrication service for cars. It is known that the mean time taken for this

Answer 1

Answer:

The answer is below

Explanation:

The z core is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by:

$z=\frac{x-\mu}{\sigma}\\\\where\ \mu=mean,\sigma=standard\ deviation$, x = raw score

Given that mean (μ) = 15 minutes per car, standard deviation (σ) = 2.4 minutes.

1) For x > 18:

$z=\frac{x-\mu}{\sigma} =\frac{18-15}{2.4} =1.25$

From normal distribution table, P(x > 18) = P(z > 1.25) = 1 - P(z < 1.25) = 1 - 0.8944 = 0.1056

2) For x < 10:

$z=\frac{x-\mu}{\sigma} =\frac{10-15}{2.4} =-2.08$

From normal distribution table, P(x < 10) = P(z < -2.08) = 0.0188

3) For x > 12:

$z=\frac{x-\mu}{\sigma} =\frac{12-15}{2.4} =-1.25$

For x < 16:

$z=\frac{x-\mu}{\sigma} =\frac{16-15}{2.4} =0.42$

From normal distribution table, P(12 < x < 16) = P(z < 0.42) - P(z < -1.25) = 0.6628 - 0.1056 = 0.5572