Question

5.6 6. (1 point) Let X be the weight of a newborm blue whale. It is known that the population mean weight is 5,000 pounds with a population standard deviation of 1,000 pounds. If a random sample of 25 newborn blue whales were weighed, and their sample mean X were calculated, find P(X 2 5,100).

Answer 1

5.6 given ,

mu = 5000, X = 5100, n = 25, sd = 1000

since (sample size) n is less than 30, we will use t distribution

(test statistics) t = (X - mu) / (sd/ sqrt(n)) = (5100 - 5000) / (1000 / sqrt(25)) = 100 / 5 = 0.2

we have to find P(X>5100)

here degree of freedom (dof) = 25 - 1 = 24

from t table:

P(X > 5100) = P (0.2, 24) = 0.8432