Question

(b) Estimate the percentage of customer accounts for which the number of days is between 22 and 32.Х(Choose one)of the customer accounts have payment made between 22 and 32 days.

Answer 1

68%

Step-by-step explanation:
`\begin{gathered} \text{mean = }\mu\text{ = 27} \\ \text{standard deviation = }\sigma\text{ = 5} \end{gathered}`

Using the empirical formula of normal distribution:

`\begin{gathered} 68\text{ \% of the data fall within }1\text{ standard deviation of the mean} \\ 95\text{ \% of the data fall within 2 standard deviation of the mean} \\ 99.7\text{ of the data fall within 3 standard deviation of the mean} \end{gathered}`
`\begin{gathered} x\text{ is betw}en\text{ 22 and 32, we are looking for the percentage} \\ 32\text{ = }27\text{ + 5} \\ 22\text{ = 27 - 5} \end{gathered}`
`\begin{gathered} \text{This can be written as: } \\ \text{32 = }\mu\text{ + 1}\sigma \\ 27\text{ = }\mu\text{ - 1}\sigma \\ \text{ 27 < x < 32 = }\mu\text{ - 1}\sigma\text{ < x < }\mu\text{ + 1}\sigma \\ 68\text{ \% of the customer accounts have payment made betw}en\text{ 22 and 32 days} \end{gathered}`