Question

The weights of newborn baby boys born at a local hospital are believed to have a normal distribution with a mean weight of 4016 grams and a standard deviation of 532 grams. If a newborn baby boy born at the local hospital is randomly selected, find the probability that the weight will be less than 5026 grams. Round your answer to four decimal places.

Answer 1

Answer:

Required Probability = 0.97062

Step-by-step explanation:

We are given that the weights of newborn baby boys born at a local hospital are believed to have a normal distribution with a mean weight of 4016 grams and a standard deviation of 532 grams.

Let X = weight of the newborn baby, so X ~ N($\mu=4016 , \sigma^{2} = 532^{2}$)

The standard normal z distribution is given by;

              Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

Now, probability that the weight will be less than 5026 grams = P(X < 5026)

P(X < 5026) = P( $\frac{X-\mu}{\sigma}$ < $\frac{5026-4016}{532}$ ) = P(Z < 1.89) = 0.97062

Therefore, the probability that the weight will be less than 5026 grams is 0.97062 .