Imagine selecting a US high school student at random. Define the random variable X = number of languages spoken by the randomly selected student. The table below gives the probability distribution of X, based on a sample of students from the US Census at School database. What is the expected average number of languages a student knows?

Find and interpret the standard deviation for the data.

Expected value = 1.457

Standard deviation = 0.671

Step-by-step explanation:

Given the data:

Language (X) : 1 2 3 4 5

P(X) 0.630 _ 0.295 _0.065_0.008_0.002

Expected value :

ΣX*P(x) = (1*0.630)+(2*0.295)+(3*0.065)+(4*0.008)+(5*0.002)

= 1.457

Standard deviation : sqrt(Var(x))

Var(X) = Σx^2p(x) - E(x)

Var(X) = (1^2*0.630)+(2^2*0.295)+(3^2*0.065)+(4^2*0.008)+(5^2*0.002) - 1.457^2

= 2.573 - 1.457^2

= 0.450151

Standard deviation = sqrt(0.450151) = 0.6709329

= 0.671

all it means is function 3

logv3(x+2)=1

rewrite in exponential form:

logb(x) = y is equal to b^y =x

b = 3, y = 1

now solve for x:

3^1 = x+2)

x = 3-2

x = 1

see the picture for the graph.