Answer to Question #120005 in Statistics and Probability for Bernard

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

Mean =60 seconds

Sd=8 seconds

N=200 patients

i) the patients taken to hospital in less than 50 seconds

$Z=\frac {x-\mu} {\sigma}$

=$\frac {50-60}{8}$

=-1.25

P(z<-1.25) is 0.10565

The number of patients out of the 200 that will be taken to the hospital are

=0.10565*200

$\approx 21 patients$

ii) More than 64 seconds

$Z=\frac{64-60}{8}$

=0.5

P(z>0.5)=0.30854 from the standard normal tables

Out of the 200 randomly selected patients

=0.30854*200

$\approx 62 patients$ will be taken to the hospital