Question

CNNBC recently reported that the mean annual cost of auto insurance is 1032 dollars. Assume the standard deviation is 214 dollars. You take a simple random sample of 90 auto insurance policies.

Find the probability that a single randomly selected value is less than 961 dollars.

P(X < 961) =

Find the probability that a sample of size n = 90 is randomly selected with a mean less than 961 dollars.

P(M < 961) =

Answer 1

Solution :

Given that ,

mean = = 1032

standard deviation = = 214

1)

P(x < 961) = P((x - ) / < (961 - 1032) / 214)

= P(z < -0.33)

= 0.3707 Using standard normal table,

Probability = 0.3707

2)

n = 90

_M = = 1032 and

_M = / n = 214 / 90 = 22.5576

P(M < 961) =   P((M - _M ) / _M < (961 - 1032) / 22.5576)

= P(z < -3.15)   Using standard normal table.   

Probability = 0.0008