Answer to Question #104162 in Statistics and Probability for Katenda

Question

Autism SA has found that 50% of people with Autism Spectrum Disorder (ASD)
struggle with social interaction. Assume we randomly select 6 people living with ASD and
use the given information to answer questions 4 to 6.

Question 4

What is the probability that only 3 people with ASD will struggle with social interaction?
(1) 0.5
(2) 0.25
(3) 0.3125
(4) 0.2344
(5) None of the above.

Question 5

What is the probability that at most 1 person with ASD will struggle with social interaction?
(1) 0.1093
(2) 0.8907
(3) 0.0937
(4) 0.0156
(5) None of the above.

Question 6

Consider statements A to C below.

(A) The expected number of people with ASD struggling with social interaction is 3.
(B) The variance of number of people with ASD struggling with social interaction is 1.5.
(C) The standard deviation of number of people with ASD struggling with social interaction is
1.225.

Which statement(s) are correct?
(1) Only A.
(2) Only B.
(3) Only C.
(4) Only A and B.
(5) A, B and C.

Answer 1

It is a Binomial distribution problem with P=0.5 and n=6.The questions will be solved using excel Binomial formula.

Question 4

P(=3)

The formula is =BINOM.DIST(3,6,0.5,FALSE) which gives 0.3125.

Question 5

P(<=1)

The formula =BINOM.DIST(1,6,0.5,TRUE) which gives 0.1093

Question 6

$E(x)=np=6\times{0.5}=3$

$Var(x)=n\times{p}\times{(1-p)}=3\times{0.5}=1.5$

$Sd=\sqrt{1.5}=1.225$

Therefore,all the three statements (A,B, and C) are correct.