Question

Consider the information below to answer questions 1 and 2.

A Therapist knows that the nbr of children that consults with her on any given day is given by the following discrete probability distribution. Let X be the number of children consulting with the Speech Therapist on any given day and P(X = x) be the associated probability.
x 1 2 3 4 5
P (X = x) 0.1 0.15 0.2 0.3 0.25

Question 1
Which of the following statements is incorrect?
(1) P that the Therapist will consult with at least one child is 1.
(2) P that the Therapist will consult with 1 child on any given day is 0.1.
(3) P that the Therapist will consult with no children on any given day is 0.
(4) P that the Therapist will consult with more than 5 children on any given day is 0.
(5) The expected number of children consulting with the Therapist on any given day is 4.

Question 2
What is the standard deviation of X?
(1) 11.01
(2) 3.45
(3) 3.32
(4) 1.65
(5) 1.28

Answer 1

Question 1.

$E(X)=0.1*1+0.15*2+0.2*3+0.3*4+0.25*5=3.45\ne4$ .

Incorrect statement: (5) The expected number of children consulting with the Therapist on any given day is 4.

Question 2.

$\sigma=\sqrt{1^2*0.1+2^2*0.15+3^2*0.2+4^2*0.3+5^2*0.25-3.45^2}=\sqrt{1.6475}\approx 1.28.$

Answer: (5) 1.28