Answer to Question #182300 in Statistics and Probability for shaantay

Question

Debonairs Pizza discovered that their Pizza delivery times are normally distributed with a mean of 45 minutes and standard deviation of 8 minutes. What is the probability that: a) The Pizza they delivered last took between 45 minutes and 50 minutes to deliver b) The next Pizza will take less than 47 minutes to deliver

Answer 1

$\mu = 45 \\ \sigma = 8$

a)

$P(45<X<50) = P(\frac{45-45}{8}<Z<\frac{50-45}{8}) \\ = P(0<Z<0.625) \\ = P(Z<0.625) -P(Z<0) \\ = 0.7340 -0.5 \\ = 0.2340$

b)

$P(X<47) = P(Z< \frac{47-45}{8}) \\ = P(Z<0.25) \\ = 0.5987$