The formula for the z-score z of a value x from a normally distributed data is given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]In this case,
[tex]\mu=56.3,\sigma=3.7[/tex]Therefore, the z-score of 47.95 is given by:
[tex]z=\frac{47.95-56.3}{3.7}\approx-2.26[/tex]Similarly the z-score of 49.05 is -1.96
The required probability is given by:
[tex]Pr(-2.257\lt x\lt-1.959)[/tex]The required probability:
[tex]Pr(-2.26\lt x\lt-1.96)=Pr(x\lt-1.96)-Pr(x\lt-2.26)[/tex]
Hence,
[tex]Pr(-2.26\lt x\lt-1.96)=0.025-0.0119=0.0131[/tex]
