Question

birth weights of babies born to full - term pregnancies follow a normal distribution with a mean weight of 7 pounds with a standard deviation of 1.05 pounds. using z - scores to standardize the given values, what percent of babies born to full - time pregnancies weigh between 6 and 9 pounds? (all problems in this edla were done using the formulas and the \by hand\ method. if you are using a calculator then round your answers to 3 decimal places and you should be able to match the correct answer.) 27.00% 00.00% 73.87% 80.02%

Explanation:

Step1: Calculate z - scores

The formula for the z - score is \(z=\frac{x-\mu}{\sigma}\), where \(\mu = 7\) (mean), \(\sigma=1.05\) (standard deviation).
For \(x = 6\):
\(z_1=\frac{6 - 7}{1.05}=\frac{-1}{1.05}\approx - 0.952\)
For \(x = 9\):
\(z_2=\frac{9 - 7}{1.05}=\frac{2}{1.05}\approx1.905\)

Step2: Use the standard normal table

The standard normal table gives \(P(Z\lt - 0.952)=0.170\) and \(P(Z\lt1.905) = 0.971\)
The probability \(P(-0.952\lt Z\lt1.905)=P(Z\lt1.905)-P(Z\lt - 0.952)\)
\(P(-0.952\lt Z\lt1.905)=0.971-0.170 = 0.801\)

Answer:

80.02% (Since \(0.801\approx80.02\%\) when rounded appropriately)