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Andrej [43]
3 years ago
15

A popular soft drink is sold in 2​-liter ​(​2000-milliliter) bottles. Because of variation in the filling​ process, bottles have

a mean of and a standard deviation of 16 ​milliliters, normally distributed. Complete parts a and b below.
Business
1 answer:
saul85 [17]3 years ago
6 0

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:

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} }

a) Given that n = 100, μ = 2000, σ = 18

For x < 1995 millimeters:

z=\frac{x-\mu}{\sigma/\sqrt{n} }=\frac{1995-2000}{18/\sqrt{100} }  =-2.78

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

z*=\frac{x-\mu}{\sigma/\sqrt{n} }\\\\1.28=\frac{x-2000}{18/\sqrt{100} }\\\\x-2000  =-2.304\\\\x=2002.3\ ml\\\\

From the normal distribution table, P(z < z

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