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

We have mean = 60 and standard deviation = 8 seconds

sample size n = 200

(A) Finding P(X<50)

=P(z<(x-mean)/sd)

= P(z<(50-60)/8)

=P(z<-1.25)

= 0.1056 ............................... using z table for -1.25

So, expected number of patients = n*p = 200*0.1056 = 21.12 21 (rounded to nearest whole number)

(B) Finding P(X>64)

=P(z>(x-mean)/sd)

= P(z>(64-60)/8)

=P(z>0.5) 1 - P(z<0.5)

= 1 - 0.6915............................... using z table for 0.5

= 0.3085

So, expected number of patients = n*p = 200*0.3085 = 61.7 68 (rounded to nearest whole number)