A youth director for a city's parks and recreations department is planning for next year's program. From a survey of city residents, the director knows that 35% of the population participate in the parks and recreations programs. For a random sample of 40 people, what is standard deviation for the sampling distribution of the sample proportions, rounded to three decimal places?

Given Information:  

Sample size = n = 40  

sample proportion = p = 35% = 0.35  

Required Information:

standard deviation of sample proportion = σ

standard deviation of sample proportion = σ = 0.075

Step-by-step explanation:  

Check if the condition np ≥  10 or n(1 - p) ≥ 10 is satisfied

np ≥ 10

40*0.35 ≥ 10

14 ≥ 10 satisfied

n(1 - p) ≥ 10

40(1 - 0.35) ≥ 10

26 ≥ 10 satisfied

Which means that distribution of sample proportion will have a mean closer to the population proportion.

The standard deviation for sample proportion is given by

Therefore, the standard deviation for the sampling distribution of the sample proportions is 0.075.

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1

it is a. 4.2 because 7.6-3.4 gets the remaining length of 4.2. i might be wrong but i am pretty sure this is the answer.