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

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3

15% chance.

step-by-step explanation:

3/10 times, the 5 year old will get a tablet. 5/10 times, the 13 yer old will get a tablet. multiply both fractions to get 15/100 times, both would have a tablet.