Question

Suppose the amount of protein in a serving of 2 eggs follows a normal distribution with mean 12 grams and standard deviation 1 gram.

Let Y denote the amount of protein in a randomly selected serving of 2 eggs. Determine the following probabilities (enter each as a decimal, and round to 4 decimal places):

P(Y>10)

P(Y≥10)

P(Y<12)

P(Y=12)

Answer 1

Y denote the amount of protein in a randomly selected serving of 2 eggs

Y follows a normal distribution with mean 12 grams and standard deviation 1

P(Y>10) =1- P(Y10)

Z-score for 10 =(10-12)/1=-2/1=-2

From standard normal tables, P(Z-2) = 0.0228

P(Y10) = P(Z-1) = 0.0228

P(Y>10) = 1-P(Y10) = 1-0.0228 = 0.9772

P(Y>10) = 0.9772

P(Y 10)

As normal distribution is continuous distribution , P(Ya)=P(Y>a) ;

therefore,

P(Y10) = P(Y>10) = 0.9772

P(Y10) = 0.9772

For Normal distribution: P(Y<Mean) =P(Z<0) =0.5;

P(Y<12) = P(Y< Mean) =0.5

P(Y<12) = 0.5

For Continuous distribution P(Y=a) = 0

As normal distribution is continuous distribution , P(Y=a)=0

Therefore,

P(Y=12) = 0