The weight of the eggs produced by a certain breed of hen is normally distributed with mean 64.5 grams (g) and standard deviation 5.9 g. If cartons of such eggs

Question

The weight of the eggs produced by a certain breed of hen is normally distributed with mean 64.5 grams (g) and standard deviation 5.9 g. If cartons of such eggs can be considered to be SRSs of size 12 from the population of all eggs, what is the probability that the weight of a carton falls between 775 g and 825 g? (Round your answer to four decimal places.)

Answer 1

Hi Christopher,

 

Assuming each carton is an SRS of size 12, the weight of a carton would be normally distributed with mean 12×64.5 g and standard deviation 5.9×√12 g. If X is the weight of a carton and Z is the standard normal random variable,

 

P(775 < X < 825)

= P((775 - 12×64.5)/(5.9×√12) < Z < (825 - 12×64.5)/(5.9×√12))

= P(0.0489 < Z < 2.4953)

 

Now you must use a standard normal table or software to compute the probability. Either way your answer will be a decimal approximation, which is why you're being asked to round your answer to four decimal places. You should get an answer slightly less than 0.5.