Question

CNNBC recently reported that the mean annual cost of auto insurance is 1050 dollars. Assume the standard deviation is 235 dollars. You take a simple random sample of 97 auto insurance policies.

Find the probability that a single randomly selected value is less than 999 dollars. 
P(X < 999) =

Answer 1

Solution :

Given that,

mean = = 1050

standard deviation = = 235

n = 97

= 1050

  =  ( /n) = (235 / 97 ) = 23.8606

( < 999 )

P ( - /) < ( 999- 1050 /23.8606)

P( z < - 51 / 23.8606 )

P ( z < -2.14 )   

Using z table

= 0.0162

Probability = 0.0162