Practise modelling a sample mean from a normal population with unchanged mean and variance σ²/n, then standardising it to calculate probabilities for sample averages.
Wendy's journey to work consists of three parts: walking to the train station, riding on the train and then walking to the office. The times, in minutes, for the three parts of her journey are independent and have the distributions N(15.0,1.12),N(32.0,3.52) and N(8.6,1.22) respectively.
Find the probability that the mean of Wendy's journey times over 15 randomly chosen days will be less than 54.5 minutes.
54.5-" 55.6 "" 14.9 "/15 or 817.5-834223.5[=-1.104]
FT their 55.6 and 14.9
No mixed methods
1- ("1.104")
For correct probability area consistent with their working
0.135(3 sf)
As final answer