Answer: 0.3446
Step-by-step explanation:
Let the random variable x is normally distributed with mean [tex]\mu= 88[/tex] and standard deviation [tex]\sigma= 5[/tex].
The required probability :[tex]P(x<86)=P(\dfrac{x-\mu}{\sigma}<\dfrac{86-88}{5})\\\\=P(Z<-0.4)=1-P(Z<0.4)\ \ \ [Z=\dfrac{x-\mu}{\sigma},\ \ \ P(Z<-z)=1-P(Z<z)]\\\\=1-0.6554\ \ \ [\text{By p-value table}]\\\\=0.3446[/tex]
Hence, P(x < 86) =0.3446
