Question

A local bank surveyed the status of ASU student accounts and found that the average overdraft was $21.22 with a standard deviation of $5.49. If the distribution is normal, find the probability of a student being overdrawn by more than $18.75.

Answer 1

Answer: the probability of a student being overdrawn by more than $18.75 is 0.674

Explanation:

Since the bank overdrafts of ASU student accounts are normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = bank overdraft of Asu students.

µ = mean

σ = standard deviation

From the information given,

µ = $21.22

σ = $5.49

We want to find the probability of a student being overdrawn by more than $18.75. It is expressed as

P(x > 18.75) = 1 - P(x ≤ 18.75)

For x = 18.75,

z = (18.75 - 21.22)/5.49 = - 0.45

Looking at the normal distribution table, the probability corresponding to the z score is 0.326

Therefore,

P(x > 18.75) = 1 - 0.326 = 0.674