Question

Please Double Check answers I've recived 3 wrong answers on three diffrent questions today thank you

CNNBC recently reported that the mean annual cost of auto insurance is 1006 dollars. Assume the standard deviation is 245 dollars. You take a simple random sample of 73 auto insurance policies.

Find the probability that a single randomly selected value is less than 973 dollars. P(X < 973) =

Find the probability that a sample of size n = 73 is randomly selected with a mean less than 973 dollars. P(M < 973) =

Answer 1

Solution:

Given that,

mean =   = 1006 doller

standard deviation =  = 245 doller

a ) P( x < 973 )

P ( x -  / ) < ( 973 - 1006 / 245)

P ( z < - 33 / 245 )

P ( z < - 0.13)

Using z table

= 0.4483

Probability = 0.4483

b ) n = 73

_M = 1006

_M =  ( /n) = (245 / 73) = 28.6751

P ( M < 973 )

P ( M -  _M/ _M) < ( 973 - 1006 / 28.6751)

P ( z < - 33 / 28.6751)

P ( z < - 1.15)

Using z table

= 0.1251

Probability = 0.1251