An engineer is going to redesign an ejection seat for an airplane. the seat was designed for pilots weighing between 130lb and 171lb. The new population of pilots has normally distributed weights with a mean of 137lb and a standard deviation of 28.9lb. If a pilot is randomly selected find the probability that his weight is between 130lb and 171lb​

Answer: 0.4758Step-by-step explanation:Given : Mean : [tex]\mu=137\text{ lb}[/tex]Standard deviation : [tex]\sigma =28.9\text{ lb}[/tex]Also, the new population of pilots has normally distributed .The formula to calculate the z-score :-[tex]z=\dfrac{x-\mu}{\sigma}[/tex]For x=130 lb .[tex]z=\dfrac{130-137}{28.9}=-0.2422145\approx-0.24[/tex]For x=171lb.[tex]z=\dfrac{171-137}{28.9}=1.1764705\approx1.18[/tex]The p-value =[tex]P(-0.24<z<1.18)=P(z<1.18)-P(z<-0.24)[/tex][tex]=0.8809999-0.4051651=0.4758348\approx0.4758348\approx0.4758[/tex]Hence, the required probability : 0.4758