Question

At a large bank, account balances are normally distributed with a mean of $1,637.52 and a standard deviation of $623.16. What is the probability that a simple random sample of 400 accounts has a mean that exceeds $1,650?

Answer 1

Solution :

Given that ,

mean = = 1637.52

standard deviation = = 623.16

n = 400

= = 1637.52 and

= / n = 623.16 / 400 = 31.158

P( > 1650) = 1 - P( < 1650)

= 1 - P(( - ) / < (1650 - 1637.52) / 31.158)

= 1 - P(z < 0.40)

= 1 - 0.6554 Using standard normal table.

= 0.3446

The probability that a simple random sample of 400 accounts has a mean that exceeds $1,650 is 0.3446.