Question

The weights of newborn baby boys born at a local hospital are believed to have a normal distribution with a mean weight of 3915 grams and a variance of 429,025. If a newborn baby boy born at the local hospital is randomly selected, find the probability that the weight will be less than 4570 grams. Round your answer to four decimal places.

Answer 1

Given that weights of newborn baby boys at a local hospital are believed to have a normal distribution with a mean weight of 3915 grams and a variance of 429,025.

Let,

X= Weight of newborn baby boys at a local hospital

Before we go on to solve the problems let us know a bit about normal distribution.

Normal Distribution

A continuous random variable X is said to have a normal distribution if its PDF(Probability Density Function) is given by

its CDF(Cumulative Distribution Function) is given by,

Notation:

Standard Normal Distribution

A continuous random variable X is said to have a standard normal distribution if its PDF(Probability Density Function) is given by

its CDF(Cumulative Distribution Function) is given by,

Exact evaluation of ?(x) is not possible but numerical method can be applied. The values of ?(x) has been tabulated extensively in Biometrika Volume I.

Notation:

Note:-

Coming back to our problem

X= Weight of newborn baby boys at a local hospital

Now we need to find the probability a randomly selected newborn baby boy born at the local hospital will be less than 4570 grams.

.

Hence the probability that a randomly selected newborn baby boy born at the local hospital will be less than 4570 grams is 0.8413