The value of a is 72.74.
Probability is the study of likeliness of an event to happen.
It is given that
The mean [tex]\rm \mu[/tex] of the distribution is 70
Standard deviation [tex]\rm \sigma[/tex] is 2
p( x<a) = 0.9147
a = ?
From Z table
For p ( p < 0.9147) , z = 1.37
[tex]\rm Z = \dfrac { X - \mu}{ \sigma}[/tex]
[tex]\rm \rm 1.37 = \dfrac { a - 70}{ 2}[/tex]
a = 70+ 2*1.37
a = 72.74
Therefore the value of a is 72.74.
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