5. The informati on below is the number of daily emergency service calls made by

Question

5. The informati on below is the number of daily emergency service calls made by the volun- n, there teer ambulance service of Walterboro, were 22 days on which there were two emergency calls, and 9 days on which there were three emergency calls. South Carolina, for the last 50 days. To expla Number of Calls Frequency 10 4 Total 50 a. Convert this information on the number of calls to a probability distribution. b. Is this an example of a discrete or continuous probability distribution? c. What is the mean number of emergency calls per day? d. What is the standard deviation of the number of calls made daily? The director of admissions at Kinzua Iniversity in Nova Scotia estimated the distribution of 6.

Explanation / Answer

Question 5

(a)Here if x is the number of emergency calls made by voluntary ambulance services on the last 50 days.

THe probability distribution is

p(x) = total number of frequency / Total days

p(x) = 8/50 = 0.16 ; x = 0

= 10/50 = 0.2 ; x = 1

= 22/50 = 0.44; x = 2

= 9/50 = 0.18 ; x = 3

= 1 /50 = 0.02 ; x = 4

(b) This is an example of discrete probability distribution.

(c) Mean number of emergency calls per day E(x) = 0.16 * 0 + 0.20 * 1 + 0.44 * 2 + 0.18 * 3 + 0.02 * 4 = 1.7

(d) Variance of x ; VaR(x) = 0.16 * (0 - 1.7)2 + 0.20 * (1 - 1.7)2 + 0.44 * (2 - 1.7)2 + 0.18 * (3 - 1.7)2 + 0.02 * (4 - 1.7)2 = 1.01

Standard deviation of x ; STD(x) = sqrt(1.01) = 1.005

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