The normal model N(58, 21) describes the distribution of weights of chicken eggs in grams. Suppose that the weight of a randomly selected chicken egg has a z-score of 1.78. What is the weight of this egg in grams

Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:

Where and

The z score for this case is given by this formula:

We know that the value of z = 1.78 and we want to estimate the value of X. If we solve for X from the z formula we got:

So the corresponging weight for a z score of 1.78 is 95.38 grams

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:

Where and

The z score for this case is given by this formula:

We know that the value of z = 1.78 and we want to estimate the value of X. If we solve for X from the z formula we got:

So the corresponging weight for a z score of 1.78 is 95.38 grams