Answer:
a) 0.1728
b) 0.09183
c) 0.7354
d) $ 222.25
Explanation:
Given
mean = = $367
Standard deviation = =$88
Cost of automobile repair is normally distributed.
a) We have to find P( x > 450 )
P( x > 450 ) = 1 - P( x <= 450 )
Using excel function, P( x <= x ) = NORMDIST (x, ,
, 1 )
P( x > 450 ) = 1 - NORMDIST( 450 , 367, 88, 1 )
= 1 - 0.8272 = 0.1728
P( x > 450 ) = 0.1728
b) P( x < 250 ) = NORMDIST( 250 , 367, 88, 1 ) = 0.09183
P( x < 250 ) = 0.09183
c) P( 250 < x < 450 ) = P( x <450 ) - P( x < 250 )
P( x <450 ) = NORMDIST( 450 , 367, 88, 1 ) = 0.8272
P( x < 250 ) = NORMDIST( 250 , 367, 88, 1 ) = 0.09183
P( 250 < x < 450 ) = 0.8272 - 0.09183 = 0.7354
P( 250 < x < 450 ) = 0.7354
d) We have P( X < a ) = 0.05
We have to find a.
Using Excel, = NORMINV ( Probability, ,
)
a = NORMINV ( 0.05 , 367, 88 ) = 222.2529
Cost = $ 222.25