Help me with this z-score question?

Question

For a sample of inmates, the mean number of misconduct violations in a month is 8, with a standard deviation of 1.5, what percentage of inmates has less misconduct violations that an inmate with 9 violation?

Answer 1

My friends, key to this Normal distribution problem is to translate where 9 falls when you normalize it.  X is normally distributed with mean = 8 and SD = 1.5

 

P ( X< 9) = P (Z < (9 - 8)/1.5) = P (Z < .667).

 

Do a look up in a normal table, .7476 or 74.76% is your result.