Answer to Question #343584 in Statistics and Probability for curties

Question

A pizza parlour will deliver a pizza take-away order to the customer if s/he lives within a 5 kilometre radius from the pizza parlour. If the customer lives within this radius, it is found that the time taken to receive the pizza is normally distributed with a mean time of 45 minutes and a standard deviation of 8 minutes. Paul has relocated and now lives within the 5 kilometre radius. He orders a pizza from the pizza parlour. The probability that it takes between 43 and 49 minutes for him to receive his pizza is (correct to 2 decimal places)

 

Answer 1

$$P(43<X<49)=P(Z<\dfrac{49-45}{8})$$

$$-P(Z\le\dfrac{43-45}{8})=P(Z<0.5)$$

$$-P(Z\le-0.25)\approx0.69146-0.40129$$

$$\approx0.29$$