Question

Pay your bills: In a large sample of customer accounts, a utility company determined that the average number of days between when a bill was sent out and when the payment was made is

29 with a standard deviation of 6 days. Assume the data to be approximately bell-shaped.

A) Between what two values will approximately 68% numbers of the days be? Approximately 68% of the customer accounts have payment made between _____ and _____ days.

Answer 1

Solution :

Given that,

mean = $\mu$ = 29

standard deviation = $\sigma$ = 6

Using standard normal table,

P(-z < Z < z) = 68%
P(Z < z) - P(Z < z) = 0.68
2P(Z < z) - 1 = 0.68
2P(Z < z ) = 1 + 0.68
2P(Z < z) = 1.68
P(Z < z) = 1.68 / 2
P(Z < z) = 0.84
z = 0.99 znd z = - 0.99

Using z-score formula,

x = z * $\sigma$ +$\mu$

x =- 0.99 * 6 + 29

= 23.06

x = 23

x = z * $\sigma$ + $\mu$

x = - 0.99 * 6 + 29

= 34.94

x = 35