Answer :
Answer:
The probability is [tex]P(X < 900 ) = 0.0918[/tex]
Step-by-step explanation:
From the question we are told that
The sample mean is [tex]\= x = 1100[/tex]
The standard deviation is [tex]\sigma = 150[/tex]
The random number value is x =900
The probability that a trainee earn less than 900 a month is mathematically represented as
[tex]P(X < x) = P(\frac{X -\= x}{\sigma} < \frac{x -\= x}{\sigma} )[/tex]
Generally the z-value for the normal distribution is mathematically represented as
[tex]z = \frac{x -\mu }{\sigma }[/tex]
So From above we have
[tex]P(X < 900 ) = P(Z < \frac{900 -1100}{150} )[/tex]
[tex]P(X < 900 ) = P( Z <-1.33)[/tex]
Now from the z-table
[tex]P(X < 900 ) = 0.0918[/tex]