the average hourly wage of workers at a mill is $6.50 with a standard deviation

Question

the average hourly wage of workers at a mill is $6.50 with a standard deviation of $0.45.  Assume thaat the distribution is normally distributed.  If a worker at this mill is selected at random, what is the probability that       A.  the worker earns more than $6.75?   B.  the worker earns between $6.00 and $7.00?    C. how much must the worker earn to be considered in the top 5% of wage earners for mill employees?

Explanation / Answer

X~Normal(=6.5, =0.45) (a) P(X>6.75) = P( (X-)/ > (6.75-6.5)/0.45)=P(Z> 0.56) = 0.2877 (check normal table) (b) P(6 (c-6.5)/0.45 =1.645 (check normal table) --> c=6.5 + 1.645*0.45 =7.24

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