Given Information:
Average number of days = 28
Standard deviation = 7
Required Information:
Between what two values will approximately 95% of the number of days be?
Solution:
Recall the Empirical Rule,
68% of the data fall within 1 standard deviation from the mean.
95% of the data fall within 2 standard deviations from the mean.
99.7% of the data fall within 3 standard deviations from the mean.
Since we are asked for 95%
Lower limit = μ - (2)σ
Upper limit = μ + (2)σ
Where μ is the average number of days and σ is the standard deviation.
Lower limit = 28 - (2)7 = 28 - 14 = 14 days
Upper limit = 28 + (2)7 = 28 + 14 = 42 days
Part (b)
Estimate the percentage of customer accounts for which the number of days is between 21 and 35.
Lower limit = 21
Upper limit = 35
Lower limit = μ - (x)σ
21 = 28 - (x)7
(x)7 = 28 - 21
(x)7 = 7
x = 7/7 = 1
Which means that 68% of the customer accounts have payment made between 21 and 35 days.
