A certain type of bacteria occurs in all raw milk. Let X be the bacteria count p

Question

A certain type of bacteria occurs in all raw milk. Let X be the bacteria count per milliliter of milk. If the milk is not contaminated, then X is a random variable with population mean = 2500 and population standard deviation = 300. In a large commercial dairy, the health department takes n random observations of the milk produced each day. The sample mean is X . Assuming the milk is not contaminated, X approximately follows a normal distribution with standard deviation 50. (i) What is the sample size n? (ii) Compute P( X larger or equal to 2650).

Explanation / Answer

a) SE = s / sqrt(n)

50 = 300 / sqrt(n)

n = 36

b) P(x > 2650)

z = ( x - mean) / s

= (2650 - 2500) / 50

= 3

Now, we need to find p(z > 3)

p (x >2650 ) = p(z >3) = 0.0013

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