Question

24.) Assume that the mean age of registered vehicles is 95 months with a standard deviation of 18 months. Find the probability that a sample of 40 vehicles has a mean age greater than 107 months. 25.) Assume that the mean age of registered vehicles is 95 months with a standard deviation of 18 months. Find the probability that a sample of 40 vehicles has a mean age less than 108 months.

Answer 1

24.

25.

Let X denotes mean for a random sample of size n =40. Here, X - Normal(95, 18.002 -) or X - Normal(95, 2.852) 40 Now, X – 95.00 P(Ã > 107.00) = 1 - P(X < 107.00) = 1 - P( 107.00 – 95.00 2.85 2.85 → P(X > 107.00) = 1 - P(Z < 107.00 – 95.00 2.85 = P(X > 107.00) = 1 - P(Z < 4.216370) → P(X > 107.00) = 1 – 0(4.216370) = P(X > 107.00) = 1 – 0.999988 = 0.000012 ~ 0.0000

Let X denotes the sample mean for a random sample of size n =40. Here, - Normal(95.00, or X ~ Normal(95.00, 2.852) Now, X - 95.000 P(X < 108.00) = P(X < 108.00) = P( 2.85 18.002 40.00 108.000 – 95.000 2.85 + P(X < 108.00) = P(Z < 108.000 - 95.000 2.85 → P(X < 108.00) = P(Z < 4.567734) → P(X < 108.00) = 0.999998 ~ 1.0000