In: Statistics and Probability
CNNBC recently reported that the mean annual cost of auto insurance is 972 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 980 dollars. P(X < 980) =
Find the probability that a sample of size n = 58 n=58 is randomly selected with a mean less than 980 dollars. P(M < 980) =
Enter your answers as numbers accurate to 4 decimal places.
Solution :
Given that ,
mean =
= 972
standard deviation =
= 238
P(x < 980) = P[(x -
) /
< (980 - 972) / 238]
= P(z < 0.03)
= 0.5120
P(x < 980) = 0.5120
M
=
/
n = 238 /
58 = 31.2509
P(M < 980) = P((M -
M) /
M < (980 - 972) / 31.2509)
P(z < 0.2560)
= 0.6026
P(M < 980) = 0.6026