Answer to Question #140974 in Statistics and Probability for Ally

Question

The average time for a courier to travel from Manila to Pampanga is 200 minutes, and the standard deviation is 10 minutes. If one of these trips is selected at random, find the probability that a courier will have the following travel time: a. At least 180 minutes b. At most 205 minutes

Answer 1

Assume that the travel times are normally distributed.

a. $P(X\ge180)$

$\mu=200,\sigma=10$

$P(X\ge180)=P(Z\ge\frac{180-200}{10})$

$=P(Z\ge-2)$

$=1-P(Z\le-2)$

$=1-0.02275$

$=0.97725$

b. $P(X\le205)$

$P(X\le205)=P(Z\le\frac{205-200}{10})$

$=P(Z\le0.5)=0.6915$