Question

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.

Answer 1

The answer is below.

Step-by-step 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=(x-\mu)/(\sigma)\\\\where\ x=raw\ score, \mu=mean,\sigma=standard\ deviation\\\\For\ a\ sample\ size(n):\\\\z=(x-\mu)/(\sigma/√(n) )`

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

For x < 1995 millimeters:

`z=(x-\mu)/(\sigma/√(n) )=(1995-2000)/(18/√(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*=(x-\mu)/(\sigma/√(n) )\\\\1.28=(x-2000)/(18/√(100) )\\\\x-2000 =-2.304\\\\x=2002.3\ ml\\\\`

From the normal distribution table, P(z < z