Question

CNNBC recently reported that the mean annual cost of auto insurance is 1004 dollars. Assume the standard deviation is 238 dollars. You take a simple random sample of 58 auto insurance policies.

Find the probability that a single randomly selected value is less than 998 dollars.
P(X < 998) =

Find the probability that a sample of size n=58n=58is randomly selected with a mean less than 998 dollars.
P(¯xx¯ < 998) =

Enter your answers as numbers accurate to 4 decimal places.

Answer 1

Answer:

Given Data

mean =    = 1004

standard deviation =   = 238

a) P(x < 998) =

= P( z < -0.0252)

= P( z < -0.03)

Using z table,

= 0.4880

b) n = 55

  

= 31.2509

= P(z < -0.19199)

= P(z < -0.19)

Using z table

= 0.4247