The average credit card debt for college seniors is $22,199 with a standard deviation of $5300. What is the probability that a sample of 30 seniors owes a mean of more than $20,200? Round answer to 4 decimal places. Answer:

Step-by-step explanation:

The number of samples is large (greater than or equal to 30). According to the central limit theorem, as the sample size increases, the distribution tends towards normal. The formula is

z = (x - µ) / (σ/√n)

Where

x = sample mean

µ = population mean

σ = population standard deviation

n = number of samples

From the information given,

µ = 22199

σ = 5300

n = 30

the probability that a senior owes a mean of more than $20,200 is expressed as

P (x > 20200)

Where x is a random variable representing the average credit card debt for college seniors.

For n = 30,

z = (20200 - 22199) / (5300/√30) =

- 2.07

Looking at the normal distribution table, the probability corresponding to the z score is 0.0197

P (x > 20200) = 0.0197