Question

In: Statistics and Probability

CNNBC recently reported that the mean annual cost of auto insurance is 1004 dollars. Assume the...

CNNBC recently reported that the mean annual cost of auto insurance is 1004 dollars. Assume the standard deviation is 278 dollars. You take a simple random sample of 55 auto insurance policies.

Find the probability that a single randomly selected value is less than 997 dollars. P(X < 997) =

Find the probability that a sample of size n = 55 is randomly selected with a mean less than 997 dollars. P( ¯ x < 997) =

Solutions

Expert Solution

Solution :

Given that ,

mean = = 1004

standard deviation = = 278

a) P(x < 997) = P[(x - ) / < (997 - 1004) / 278]

= P(z < -0.03)

Using z table,

= 0.4880

b) n = 55

=   = 1004

= / n = 278 / 55 = 37.49

P( < 997) = P(( - ) / < (997 - 1004) / 37.49)

= P(z < -0.19)

Using z table

= 0.4247


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