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
