Answer to Question #344712 in Statistics and Probability for Emssy

Question

The average age of public jeepneys plying in Metro Manila is 15 years. Assume that the standard deviation is 8 years. If a random sample of 25 public jeepneys is chosen, Find the probability that the mean of jeepneys ages is between 12 and 19.

Answer 1

$$P(12<X<19)=P(Z<\dfrac{19-15}{8/\sqrt{25}})$$ $$-P(Z\le\dfrac{12-15}{8/\sqrt{25}})$$ $$=P(Z<2.5)-P(Z\le-1.875)$$ $$\approx0.99379-0.03034\approx0.9634$$