A study was recently conducted on the reaction time of long-distance truck drivers (after two hours of non-stop driving). Assume reaction times (after two hours of non-stop driving) are known to be normally distributed, with a mean of 1.4 seconds and a variance of 0.0625 seconds. Reaction times would be recorded (in seconds between the presentation of a stimulus and braking) by subjecting a truck driver to a simulated environment.
(a) What is the probability that a particular truck driver who has been driving for two hours non-stop has a reaction time of:
(i) more than two seconds?
(ii) between 1.2 and 1.4 seconds?
(iii) less than 0.9 seconds?
(iv) between 0.5 and one second?
(b) If a random sample of 120 truck drivers is drawn on the Golden Highway Plaza (N1, near Johannesburg), what percentage are likely to have a reaction time slower than 1.8 seconds? How many truck drivers does this represent?
(c) The National Transport Department is implementing a policy that requires truck drivers to undergo further training if their reaction time is slower than 1.7 seconds. How many drivers out of a random sample of 360 are likely to need further training?
Note: Use the z-tables and then the Excel function NORMDIST to answer the questions.