Question

A major credit card company has determined that its customers charge an average of $280 per month on their accounts with a standard deviation of $20. What percentage of the customers charges more than $275 per month?

59.87%

22.66%

40.13%

77.34%

Answer 1

given data,
customers charge an average of $280 per month
on their accounts with a standard deviation of $20
the PDF of normal distribution is = 1/σ * √2π * e ^ -(x-u)^2/ 2σ^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd ~ N(0,1)
mean ( u ) = 280
standard Deviation ( sd )= 20
percentage of the customers charges more than $275 per month
P(X > 275) = (275-280)/20
= -5/20 = -0.25
= P ( Z >-0.25) From Standard Normal Table
= 0.5987
= 59.87%

option:A