Answer to Question #96120 in Statistics and Probability for Crystal Lopez

Question

The weights of newborn baby boys born at a local hospital are believed to have a normal distribution with a mean weight of 3252 grams and a standard deviation of 614 grams. If a newborn baby boy born at a local hospital is randomly selected, find the probability that the weight will be less than 3804 grams. Round your answer to four decimal places.

Answer 1

Answer:

0.8157

Solution

To find this probability we must calculate the value of a cumulative distribution function for the normal random variable X, with parameters µ and σ. We can reduce this calculation to one concerning the standard normal random variable Z as follows:

F_X(x) = P(X ≤ x) = P(Z ≤ $\frac{x-μ}σ$ ) = F_Z($\frac{(x-μ)}σ$ )

This last expression can be found in a table of values of the cumulative distribution function for a standard normal random variable.

In our case μ = 3252, σ = 614, x = 3804, so we have

P(X < 3804) = P(X ≤ 3804) = F_Z($\frac{3804-3252}{614}$ ) = F_Z(0.8990) = 0.8157.