Nationwide, the amount charged by doctors for performing a particular minor surg

Question

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:

Explanation / Answer

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.

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