There are 50,000 households in a certain city. the average number of persons aged 16 and over living in each household is known to be 2.38, the sd is 1.87. a survey organization plans to take a simple random sample of 400 households and interview all persons age 16 and over living in the sample households. the total number of interviews will be or so.

The total number of interviews will be about 9552, give or take 37.4 or so.

Step-by-step explanation:

Data given

Total of 50000 households

represent the average  number of people in household

represent the sample standard deviation of the number of people in household

n= 400 represent the sample size.

Solution to the problem

We can assume that the sample of 400 households are selected using random sampling from a grand box of 50000, and we select 400.

The expected value for the average number of people in a household is 2.38 and the standard deviation is 1.87.

We ar einterested on this case on the expected value for the sum and is defined as:

Expected value sum = Number selected * Expected value= 400*2.38=952

The reason of this is this one: From the definition of sample mean we have:

Where T represent the sum or the total, if we solve for T we got:

Assuming that and if we find the expected value for the total and the variance we got:

And the deviation would be:

And now the standard error for the sum is defined as the product of the square root of n and the single deviation of a box like this:

So then the correct answer would be:

The total number of interviews will be about 9552, give or take 37.4 or so.

"standard form:

3x2 + 14x − 10 = 0

solutions based on quadratic formula:

x1   = −14 − √ 142 − 4×3×(−10) /   2×3   = −14 − 2 × √ 79 /   6   ≈ −5.296

x2   = −14 + √ 142 − 4×3×(−10) /   2×3   = −14 + 2 × √ 79 /   6   ≈ 0.629