Question

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.

Answer 1

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