Answer: Between $9,690.1 and $10,309.9 monthly
Step-by-step explanation:
To calculate confidence interval, we apply this formula:
M ± Z* (σ/√N)
Where M is sample mean; Z is the appropriate value given in the standard normal distribution table at various confidence levels. At 95% confidence level, Z is 1.96. σ population standard deviation; N is sample size.
We know that sample mean is 10,000; sample size is 40; population standard deviation is 1000. We substitute relevant values into the formula
=10,000 ± 1.96(1000/√40)
=10,000 ± 309.903
Note that 309.903 is referred to in statistics as the margin of error
Thus, the lower limit of 95% confidence interval of the population mean given these values is
10000 – 309.903= $9,690.097
Thus, the upper limit of 95% confidence interval of the population mean given these values is 10000 + 309.903= $10,309.903
Statistical interpretation of this result is that we are 95% confident that the average sales per sale person in the pharmaceutical company lies between $9,690.1 and $10,309.9 monthly.