Answer to Question #266313 in Statistics and Probability for Moses

Question

The times that cars took to refuel at a busy service station are normally distributed with mean 3

minutes and a standard deviation of 0.5 minutes. What is the probability that a car will take

(a) more than 4 minutes to refuel,

(b) not more than 2 minutes to refuel,

Answer 1

$\mu= 3 \\ \sigma = 0.5$

(a)

$P(X>4) = 1 -P(X<4) \\ = 1 -P(Z< \frac{4-3}{0.5}) \\ = 1 -P(Z< 2) \\ = 1 -0.9772\\ = 0.0228$

(b)

$P(X<2) = P(Z< \frac{2-3}{0.5}) \\ = P(Z< -2) \\ = 0.02275$