Question

Assume the credit card balances of younger college educated employed persons are normally distributed with a mean of $ 6,358 and a standard deviation of $1,907 – assume these are population values. 2. Now you randomly select 81 credit card holders. What is the probability that their mean credit card balance is less than $5750? Use the standard normal table for this, but this time use the population mean and standard error (standard deviation/SQRT(81)). Use 4 significant decimal places for your answer, and use the proper rules of rounding. I am looking for just the answer, not the equation.

Answer 1

Using central limit theorem,

P($\bar{x}$ < x) = P( Z < x - $\mu$ / $\sigma$ / sqrt(n) )

So,

P($\bar{x}$ < 5750) = P (Z < 5750 - 6358 / ( 1907 / sqrt(81) ) )

= P( Z < -2.8694)

= 0.0021 (from Z table )