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.

its 50 miles away from the starting point

57.09 minus 7.0435 equals

step-by-step explanation:

just subtrach them both and u get the answer of 50.0465