Question

PLEASE help me with this algebra multiple choice question I have been stuck on and if possible, give an explanation:

Times for an ambulance to respond to a medical emergency in a certain town are normally distributed with a mean of 400 seconds and a standard deviation of 50 seconds.
Suppose there are 144 emergencies in that town.
In about how many emergencies are the response times expected between 350 seconds and 450 seconds?

A) 49

B) 51

C) 96

D) 98

Answer 1

D

Explanation:

First find the probability using the normal distirbution formula X - mean / standard deviation for both X = 350 and X =450 to get the values -1 and 1 so thi(-1) < P(Z) < thi(1) if you are familiar with normal distirbution table values you will calculate that the overall probability is 0.6827

knowing this we can roughly expect how much emergencies are in the response times by 0.6827 x 144 = 98

Answer 2

D) 98

Explanation:

Here we will use Empirical formula for solving this question.

Calculating:
`(350-400)/(50)=-1 and (450-400)/(50) =1`

Since 68% of the data lies in the one standard deviation of the mean.

Also, there are 144 emergencies in the town. So,

0.68 × 144 = 97.92 ≈ 80

Thus, Option D is correct.