Answer:
The answer is below.
Explanation:
The z score is a used in statistics 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\ x=raw\ score, \mu=mean,\sigma=standard\ deviation\\\\For\ a\ sample\ size(n):\\\\z=\frac{x-\mu}{\sigma/\sqrt{n} }[/tex]
a) Given that n = 100, μ = 2000, σ = 18
For x < 1995 millimeters:
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{1995-2000}{18/\sqrt{100} } =-2.78[/tex]
From the normal distribution table, P(x < 1995) = P(z < -2.78) = 0.0027
b) P(z > z*) = 10% = 0.1
P(z < z*) = 1 - 0.1 = 0.9
z* = 1.28
[tex]z*=\frac{x-\mu}{\sigma/\sqrt{n} }\\\\1.28=\frac{x-2000}{18/\sqrt{100} }\\\\x-2000 =-2.304\\\\x=2002.3\ ml\\\\[/tex]
From the normal distribution table, P(z < z
