In: Math
The population average cholesterol content of a certain brand of egg is 215 milligrams, and the standard deviation is 15 milligrams. Assume the variable is normally distributed.
If we are told the average for 25 eggs is less than 220 mg, what is the probability that the average is less than 210?
Round the answers to four decimal places.
Solution:
Given that,
mean = = 215 miligrams
standard deviation = = 15 miligrams
n = 25
= 215
= (
/
n) = (15 /
25 ) = 3
p ( < 220 )
= p ( -
/
) < (220 - 215 / 3 )
= p ( z < 5 / 3 )
= p ( z < 1. 67 )
Using z table
= 0.9525
Probability = 0.9525
p ( < 210 )
= p ( -
/
) < (210 - 215 / 3 )
= p ( z < - 5 / 3 )
= p ( z < - 1. 67 )
Using z table
= 0.0475
Probability = 0.0475