Question

Assume that the cost for an automobile repair is normally distributed with a mean of $370 and standard deviation of $82. What is the probability that the cost will be between $225 and $475?

Answer 1

Solution :

Given that,

mean = = 370

standard deviation = =27

P (225 < x < 475 )

P ( 225 - 370 / 82) < ( x -  / ) < ( 475 - 370 / 82)

P (-145 / 82 < z < 105 / 82 )

P (-1.77 < z < 1.28)

P ( z < 1.28 ) - P ( z < -1.77)

Using z table

= 0.8997 - 0.0384

= 0.8613

Probability = 0.8613