Question

Veterinary costs for standard veterinary services at a local animal hospital follow a normal distribution with a mean of $80 and a standard deviation of $20. (a) Find the proportion of costs that will be greater than $95. (b) Find the proportion of costs that will be less than $60. (c) Find the range of costs that would represent the middle 90% of costs.

Answer 1

(47.1, 112.9)

Explanation:

Let X be the veterinary costs for standard veterinary services at a local animal hospital

X is N(80, 20)

a) the proportion of costs that will be greater than $95.

=
`P(X>95)\\\\= P(z>0.75)\\\\==0.2266`

b) the proportion of costs that will be less than $60

=
`P(X<60)\\= 0.1587`

c) 90% of normal costs would be between

-1.645 <Z<1.645

Corresponding x scores are

`80`±32.9

=(47.1, 112.9)