Answer: 0.5237
Step-by-step explanation:
Mean : [tex]\mu=192\text{ days}[/tex]
Standard deviation : [tex]\sigma = 12\text{ days}[/tex]
The formula to calculate the z-score is given by :-
[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
For x = 188 days ,
[tex]z=\dfrac{188-192}{12}\approx-0.33[/tex]
For x = 107 miles per day ,
[tex]z=\dfrac{107-92}{12}=1.25[/tex]
The P-value =[tex]P(-0.33<z<1.25)=P(z<1.25)-P(z<-0.33)[/tex]
[tex]0.8943502-0.3707=0.5236502\approx0.5237[/tex]
Hence, The probability that a randomly selected pregnancy lasts less than 188 days is approximately 0.5237.
