The weekly salary paid to employees of a small company that supplies? part-time
ID: 3376129 • Letter: T
Question
The weekly salary paid to employees of a small company that supplies? part-time laborers averages ?$750 with a standard deviation of ?$350.
?(a) If the weekly salaries are normally? distributed, estimate the fraction of employees that make more than ?$400 per week. ANSWER MUST BE A FRACTION!
?(b) If every employee receives a? year-end bonus that adds ?$100 to the paycheck in the final? week, how does this change the normal model for that? week? ?
(c) If every employee receives a 5?% salary increase for the next? year, how does the normal model? change?
?(d) If the lowest salary is ?$400 and the median salary is ?$575?, does a normal model appear? appropriate?
Explanation / Answer
a)
as we know that z score =(X-mean)/std deviation
fraction of employees that make more than ?$400 per week =P(X>400)=1-P(X<400)=1-P(Z<(400-750)/350)
=1-P(Z<-1)=1-0.1587=0.8413
b)
if every employee receives a? year-end bonus that adds ?$100 to the paycheck in the final? week ; mean will increease by 100 to $850 and std deviation will remain same as 350
c)
for 5?% salary increase for the next? year, mean will become =1.05*750=787.5 and std deviaiton =1.05*350=367.5
d)
as for normal distribution; data should be symmetric or median and means should be approximately same.
cause here mean is not equal to median ; therefore normal model should not be appropriate,
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