Suppose that 50% of people frequently exceed the speed limit. A random sample of 2000 people is surveyed and 55% indicate that they frequently speed. What is the value of the population percent given to you in the problem?

1,037 it is simple math.

I got 1100 - I multiplied 2000 by 55% guess that is wrong!!

To find the value of the population percent given the information provided, we can use the concept of sample proportion.

First, let's define some variables:
- p: Population percent of people who frequently exceed the speed limit
- p̂: Sample proportion, which is the percent of people in the sample who indicate that they frequently speed
- n: Sample size, which is the number of people surveyed in the sample

According to the problem, 50% of people in the entire population frequently exceed the speed limit. Therefore, p = 0.50.

The sample proportion, p̂, is calculated by dividing the number of people in the sample who indicate that they frequently speed by the total sample size (2000 people in this case).

p̂ = 55% = 0.55

Now, we can use the formula for the standard error of a proportion to calculate the margin of error:
SE = sqrt((p̂ * (1 - p̂)) / n)

Using the given values, the standard error (SE) can be calculated as:
SE = sqrt((0.55 * (1 - 0.55)) / 2000)

Once we have the standard error, we can calculate the margin of error (ME), which is the amount to add and subtract from the sample proportion to obtain the confidence interval.
ME = z * SE

The z-value represents the desired level of confidence. For a 95% confidence level, which is commonly used, the z-value is approximately 1.96.

ME = 1.96 * SE

Finally, the confidence interval can be calculated by subtracting and adding the margin of error from the sample proportion:
CI = p̂ - ME, p̂ + ME

The population percent lies within this confidence interval.

Now, let's calculate the value of the population percent using the formula:

SE = sqrt((0.55 * (1 - 0.55)) / 2000)
ME = 1.96 * SE

CI = p̂ - ME, p̂ + ME

Lower bound of CI = 0.55 - ME
Upper bound of CI = 0.55 + ME

To find the population percent, we need to check if the lower bound of the confidence interval is less than or equal to 0.50 and if the upper bound of the confidence interval is greater than or equal to 0.50.

By performing the calculations, if the lower bound is less than or equal to 0.50 and the upper bound is greater than or equal to 0.50, then the population percent given in the problem is 50%.