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:
[tex]z=\frac{x-\mu}{\sigma}\\\\where\ \mu=mean,\sigma=standard\ deviation[/tex], x = raw score
Given that mean (μ) = 15 minutes per car, standard deviation (σ) = 2.4 minutes.
1) For x > 18:
[tex]z=\frac{x-\mu}{\sigma} =\frac{18-15}{2.4} =1.25[/tex]
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:
[tex]z=\frac{x-\mu}{\sigma} =\frac{10-15}{2.4} =-2.08[/tex]
From normal distribution table, P(x < 10) = P(z < -2.08) = 0.0188
3) For x > 12:
[tex]z=\frac{x-\mu}{\sigma} =\frac{12-15}{2.4} =-1.25[/tex]
For x < 16:
[tex]z=\frac{x-\mu}{\sigma} =\frac{16-15}{2.4} =0.42[/tex]
From normal distribution table, P(12 < x < 16) = P(z < 0.42) - P(z < -1.25) = 0.6628 - 0.1056 = 0.5572
