Question

A bank has kept records of the checking balances of its customers and determined that the average daily balance of its customers is $300 with a standard deviation of $48, and is a normally distributed population. A random sample of 144 checking accounts is selected.

a) What is the probability that the sample mean will be at least $306.60

Answer 1

Solution :

Given that ,

mean = = 300

standard deviation = = 48

n = 144

= 300 and

= / n = 48 / 144 = 48 / 12 = 4

(a)

P( ) = 1 - P( 306.60)

= 1 - P(( - ) / < (306.60 - 300) / 4)

= 1 - P(z < 1.65)

= 1 - 0.9505

= 0.0495

P( > 306.60) = 0.0495

Probability = 0.0495