What is best time to apply as Bank Teller?

The lengths of time bank customers must wait for a teller are normally distributed, with a mean of 3 minutes a?

• 8. The lengths of time bank customers must wait for a teller are normally distributed, with a mean of 3 minutes and a standard deviation of 1 minute. a. What proportion of bank customers waits between 3 and 4.5 minutes b. What percentage wait more than 4 minutes? c. What proportion waits between 2 and 3.5 minutes? d. What percentage wait less than 1 minute?

• Answer:

  (4.5 - 3) / 1 = z 1.5 = z P(z = 1.5) = 0.933192799 (3 - 3) / 1 = z 0 = z P(z = 0) = .5 P(3 < x < 4.5) = .933192799 - .5 P(3 < x < 4.5) = .433192799 A) 43.32% (4 - 3) / 1 = z 1 = z P(z = 1) = 0.841344746 P(x > 4) = 1 - 0.841344746 P(x > 4) = 0.158655254 B) 15.87% (3.5 - 3) / 1 = z .5 = z P(z = .5) = 0.691462461 (2 - 3) / 1 = z -1 = z P(z = -1) = 0.158655254 P(2 < x < 3.5) = .691462461 - .158655254 P(2 < x < 3.5) = 0.532807207 C) 53.28% (1 - 3) / 1 = z -2 = z P(z = -2) = 0.022750132 P(x < 1) = 0.022750132 D) 2.28%