Random variable X is the weekly amount of money spent on ma

) Random variable X is the weekly amount of money spent on maintenance by a company, it was observed to be normally distributed, that is, X N(4500, 400^2 ).

(a) If $5000 is budgeted for next week, what is the probability that the actual cost will exceed the budgeted amount $5000?

(b) I hope the probability that the budged will be exceeded is 0.008, What is the budget amount you should make? That is, find the value k such that P(X > k) = 0.008.

Solution

Normal Distribution
Mean ( u ) =4500
Standard Deviation ( sd )=400
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
a)
P(X > 5000) = (5000-4500)/400
= 500/400 = 1.25
= P ( Z >1.25) From Standard Normal Table
= 0.1056                  
b)
P ( Z > x ) = 0.008
Value of z to the cumulative probability of 0.008 from normal table is 2.41
P( x-u/ (s.d) > x - 4500/400) = 0.008
That is, ( x - 4500/400) = 2.41
--> x = 2.41 * 400+4500 = 5463.6