Question

The time required by Amazon’s new Phoenix warehouse to pick a small sized order (<4 items) is an important measure of efficiency and customer service. The staff obtained 50 samples, resulting in an average of 20.5 minutes. Based on its many warehouses, the standard deviation is known to be 6 minutes. Develop a 95% and a 99% confidence interval of the time to pick small orders at the Phoenix warehouse.

Answer 1

a)

95% confidence interval for $\mu$ is

$\bar{x }$ - Z * $\sigma$ / sqrt(n) < $\mu$ < $\bar{x }$ + Z * $\sigma$ / sqrt(n)

20.5 - 1.96 * 6 / sqrt( 50) < $\mu$ < 20.5 + 1.96 * 6 / sqrt( 50)

18.837 < $\mu$ < 22.163

95% CI is (18.837 , 22.163)

b)

99% confidence interval for $\mu$ is

$\bar{x }$ - Z * $\sigma$ / sqrt(n) < $\mu$ < $\bar{x }$ + Z * $\sigma$ / sqrt(n)

20.5 - 2.576 * 6 / sqrt( 50) < $\mu$ < 20.5 + 2.576 * 6 / sqrt( 50)

18.314 < $\mu$ < 22.686

99% CI is ( 18.314 , 22.686)