Answer:
a) 0.5085
b) -1.6551
c) 0.8103834
Step-by-step explanation:
Data provided in the question:
Mean = $19,800
Standard deviation, s = $2,900
Now,
z score = [ X - Mean ] ÷ s
a) The procedure costs between $18,000 and $22,000
For X = $22,000
z-score = [ $22,000 - $19,800 ] ÷ $2,900
= 0.7586
For X = $18,000
z-score = [ $18,000 - $19,800 ] ÷ $2,900
= -0.62069
P(procedure costs between $18,000 and $22,000)
= P(z < 0.7586) - P( z < -0.62069)
= 0.7759541 - 0.2674018 [ P value from standard z table ]
= 0.5085
b) The procedure costs less than $15,000
For X = $15,000
z-score = [ $15,000 - $19,800 ] ÷ $2,900
= -1.6551
thus,
The procedure costs less than $15,000
P (z < -1.655172 )
= 0.0489448 [ P value from standard z table ]
c) The procedure costs more than $17,250
z-score = [ $17,250 - $19,800 ] ÷ $2,900
= -0.87931
thus,
The procedure costs more than $17,250.
P (z > -0.87931 ) = 0.8103834
