Chapter 11.10, Problem 1.3A

Solution

To find: The probability that a newborn weighs between 2270 g and 4230 g.

The probability is 0.95

Given information:

In a given population,the weights of newborns are normally distributed about the mean 3250 g. The standard deviation of the population is 500 g.

The normal curve for z -scores is given by:

  

Calculation:

The z -score of a data point is given by $z=\frac{x-\mu }{\sigma }$ .

Here, $x=2270,\mu =3250,\sigma =500$

Plugging the values:

  $\begin{array}{c}z=\frac{2270-3250}{500}\\ =\frac{-980}{500}\\ =-1.96\end{array}$

And, $x=4230,\mu =3250,\sigma =500$

Plugging the values:

  $\begin{array}{c}z=\frac{4230-3250}{500}\\ =\frac{980}{500}\\ =1.96\end{array}$

The z -score for the given weights is between -1.96 and 1.96.

From the normal curve, the percentage of population between the scores is:

  $\begin{array}{l}p=13.5+34+34+13.5\\ p=95\%\end{array}$

Hence the probability is 0.95

Conclusion:

The probability is 0.95