It is given that the mean is 79.1 inches and standard deviation is 3.0 inches so it follows:
[tex]\mu=79.1,\sigma=3[/tex]So the value from 75 to 81 is given by:
[tex]\begin{gathered} P(75\leq x\leq81)=P(x\leq81)-P(x\leq75) \\ =P(z\leq\frac{81-79.1}{3})-P(z\leq\frac{75-79.1}{3}) \\ =P(z\leq0.63)-P(z\leq-1.36) \end{gathered}[/tex]Use the table or a software to get the probability values and substitute to get the probability value as:
The probability is 0.6509.
