Credit card balances follow a nearly normal distribution with a mean of $2,900 and a standard deviation of $860. A local credit union believes their customers are carrying an above average credit card balance, so they carry out a study to determine their customers' debt. If the study results in a standard error of $43, what sample size was used in the study

A sample size of 400 was used in the study.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean and standard deviation(standard error) .

In this problem, we have that:

We have to find n.

A sample size of 400 was used in the study.

y= -

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.