Answer:
The lowest score you can earn and still be eligible for employment is 85.70.
Step-by-step explanation:
We are given that Scores for a civil service exam are normally distributed with a mean of 75 and a standard deviation of 6.5.
Also, to be eligible for civil service employment, you must score in the top 5%.
<em>Let X = Scores for a civil service exam</em>
SO, X ~ N()
The z-score probability distribution is given by ;
Z = ~ N(0,1)
where, = mean score = 75
= standard deviation = 6.5
Now, the lowest score that we can earn and still be eligible for employment is given by ;
P(X ) = 0.05 {where is minimum score required}
to be in top 5%}
P( ) = 0.05
P(Z ) = 0.05
<em>Now, in z table we will find out that critical value of X for which the area is in top 5%, which comes out to be </em><u><em>1.6449.</em></u><em> </em>
This means;
= 75 + 10.69185 = 85.70
Therefore, the lowest score that we can earn and still be eligible for employment is 85.70.