Answer to Question #120098 in Statistics and Probability for Ernestina

Question

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

Time~N(60, 8²)

N=200 patients

i) The number of patients taken to hospital in less than 50 seconds are

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

$=\frac {50-60}{8}$ =-1.25

P(z<-1.25) is 0.10565 from the z tables and

0.1057*200 patients

≈21 patients

ii) the number of patients taken in more than 64 seconds

$Z=\frac{64-60}{8}$ = 0.5

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

0.3085*200 patients

≈62 patients