SOLUTION: CNNBC recently reported that the mean annual cost of auto insurance is 1002 dollars. Assume the standard deviation is 278 dollars. You take a simple random sample of 76 auto insura

Algebra ->  Probability-and-statistics -> SOLUTION: CNNBC recently reported that the mean annual cost of auto insurance is 1002 dollars. Assume the standard deviation is 278 dollars. You take a simple random sample of 76 auto insura      Log On


   

Question 1177992: CNNBC recently reported that the mean annual cost of auto insurance is 1002 dollars. Assume the standard deviation is 278 dollars. You take a simple random sample of 76 auto insurance policies.
Find the probability that a single randomly selected value is less than 981 dollars.
P(X < 981) =

Find the probability that a sample of size
n
=
76
is randomly selected with a mean less than 981 dollars.
P(M < 981) =

Enter your answers as numbers accurate to 4 decimal places.
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
P(x<981); z=(x-mean)/sd; 981-1002=-21
z < -21/278=-0.0755
probability is 0.4699
-
sample mean <981 is z=(x bar-mean)/sigma/sqrt(n)
z < (-21)/278/sqrt(76)
=(-21/278)*(sqrt(76)/278=-0.6585
probability z < -0.6585=0.2551
Much less likely that the mean of a sample of 76 will be as small as 981 or less.
The fourth decimal place will change depending on the rules given for rounding z. If to two places, it will be different from the values here.