Question

Given that 10% of us are left-handed and some desks are amde for left-handed students. To determine the number ofsuch desks to order and place in our classrooms, we want to compute the probability of getting exactly 3 left-handed studetns in a class of 15.

a) This a a binomial experiemnt. Explain why.

b) Use the binomial probability formula to find the probability of getting 3 left-handed students in a class of 15 students, given that 10% of us are left-handed.

c)Generate the probability distribution for eaach random variable for this experiment.

d) Find the mean and standard deviation for this event.

Answer 1

a)her number of trails =15 are fixed,

probability of success 0.1 is fixed from trail and trail and independent,

number of outcomes are 2, left handed or not left handed

therefore this is a binomial experiment

b)

P(X=3)=(₁₅C₃)*(0.1)³*(0.9)¹² =0.2059

c_)

below is probability mass function table for this"

x	P(x)
0	0.2059
1	0.3432
2	0.2669
3	0.1285
4	0.0428
5	0.0105
6	0.0019
7	0.0003
8	0.0000
9	0.0000
10	0.0000
11	0.0000
12	0.0000
13	0.0000
14	0.0000
15	0.0000

d)

mean E(x)=μ=np=15*0.1 =1.5

standard deviation σ=√(np(1-p))=sqrt(15*0.1*0.9)=1.1619