Homework SourseNationwide the amount charged by doctors for performing a pa
Nationwide, the amount charged by doctors for performing a particular minor surgical procedure averages $1220 and varies with a standard deviation of $270. We randomly select 140 bills from the population of all bills charged for this surgery.
A) the probability the average amount charged over these 140 procedures is more than $2000 is:
B) the probability the amount charged over this procedure is between $1100 and $1300 is:
Nationwide, the amount charged by doctors for performing a particular minor surgical procedure averages $1220 and varies with a standard deviation of $270. We randomly select 140 bills from the population of all bills charged for this surgery.
A) the probability the average amount charged over these 140 procedures is more than $2000 is:
B) the probability the amount charged over this procedure is between $1100 and $1300 is:
A) the probability the average amount charged over these 140 procedures is more than $2000 is:
B) the probability the amount charged over this procedure is between $1100 and $1300 is:
Solution
Mean = 1220
SD = 270
We need P ( X > 2000 )
n = 140
We calculate Z-score :
Z = ( 2000 - 1220 ) / ( 270 / sqrt(140) )
= 34.18
P (Z > 34.18 )
= 1 - P (Z < 34.18)
which will be approximately 0 ( a very very small number actually )
b)
We calculate Z-scores for both
Z = 1100 - 1220 / ( 270 / sqrt(140) ) = -5.258
Z = 1300 - 1220 / ( 270 / sqrt(140) ) = 3.505
P ( -5.258 < Z < 3.505 )
= P (Z < 3.505) - P (Z < -5.258)
= 0.9990 - (7.275*10-8)
~ 0.9990
Hope this helps.
