Question

Name Problem 1(10 pointa) The probabilities and the number of prescription refills for a typical pharmacy is given below: Probability Number 0.10 1 0.30 2 0.25 0.20 4 0.15 a) On a typical day, how many refills on average should a typical pharmacy expect to do? b) What is the Standard Deviation of this study?

Answer 1

X: Number of Prescription refills for a typical pharmacy

Given:

X:Number	P(X)
0	0.10
1	0.30
2	0.25
3	0.20
4	0.15

(a)

Number of refills on an average a typical pharmacy Expected to do = E(X)

Number of refills on an average a typical pharmacy Expected to do = 2

(b)

Standard deviation:

Standard deviation = 1.2247

Answer 2

SOLUTION :

Average refills on a day, m :

= Sum (p * x) 

= 0.10 * 0 + 0.30 * 1 + 0.25 * 2 + 0.20 * 3 + 0.15 * 4

= 2 number of prescriptions (ANSWER).

Variance

= Sum (p * (x - m)^2 )

= 0.10*(0 - 2)^2+0.30*(1 - 2)^2+0.25*(2 - 2)^2++0.20*(3 - 2)^2++0.15*(4 - 2)^2

= 1.5

SD 

= sqrt(variance) 

= sqrt(1.5)

= 1.2247 number of prescriptions (ANSWER)