The weekly salary paid to employees of a small company that supplies part-time l
ID: 3255606 • Letter: T
Question
The weekly salary paid to employees of a small company that supplies part-time laborers averages $700with a standard deviation of $300. (a) If the weekly salaries are normally distributed, estimate the fraction of employees that make more than $400 per week. (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 $550, does a normal model appear appropriate?Explanation / Answer
Average of weekly salary = $ 700 and standard deviation = $ 300
(a) Fraction of employees that take more than $400 per week
= Pr ( salary > 400 ; 700; 300) by normal distribution
Z - value = (400 - 700)/300 = -1
so Pr ( salary > 400 ; 700; 300) = 1 - (-1) = 1 - 0.1587 = 0.8413
(b) The addition of $100 paycheck in final week will change the mean weekly salary paid to employee by $ 100, so in this case mean weekly salary week is $ 800 .
(c) Every emoployee receives 5% salary increase for the next year then mean and standard deviation both will increase by 5%,
so Changed mean value of salary = 700 * 1.05 = $735
Changed standard deviation of salary = 300 * 1.05 = $ 315
(d) Lowest salary = $400 and median salary = $550
The normal model doesn't appear appropriate as difference between mean and median is too large for normal model appropriate.
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