Question

(2b) The average time taken for the nearest Covid-19 ambulance team to convey a patient showing
symptoms to the nearest designated hospital follows the normal distribution about a mean of 60
seconds and a standard deviation of 8 seconds. If 200 patients were selected at random, how many of
them could be taken to the hospital in
i) Less than 50 seconds
ii) More than 64 seconds

Answer 1

$Given \; that, μ=60, σ=8, n=200, then,\\ ii) P(x<50)=P(Z<\frac{50-60}{8})\\ =P(Z<-1.25)=0.5-P(0<Z<1.25)\\ =0.5-0.3944=0.1056\\ number\;of\;patients=200\times0.1056=21.12\approx22\\ ii) P(x>64)=P(Z>\frac{64-60}{8})\\ =P(Z>0.5)=0.5-P(0<Z<0.5)\\ =0.5-0.1915=0.3085\\ number\;of\;=200\times0.3085=61.7\approx62\\$