A recent Gallup poll showed the president’s approval rating at 60%. Some friends use this information (along with the sample size from the poll) and find theory-based confidence intervals for the proportion of all adult Americans that approve of the president's performance.
Of the following four confidence intervals, identify the ones that were definitely done incorrectly. (There may be more than one interval that is incorrect.)

a. (0.58, 0.62)
b. (0.47, 0.53)
c. (0.60, 0.66)
d. (0.57, 0.63)

Option "b" and "c" are done incorrectly

Step-by-step explanation:

The options for the confidence interval are:

a. (0.58, 0.62)

b. (0.47, 0.53)

c. (0.60, 0.66)

d. (0.57, 0.63)

The poll showed that the president’s approval rating is 60%.

Without any calculation, we know that the confidence interval should be symetrical around the mean value (0.60).

The options "a" and "d" are symetrical, but "b" and "c" are not.

We can say then that both option "b" and "c" are done incorrectly.

To evaluate "a" and "d" we need the sample size.