Basic Statistics20815 marksNumerical: normal distribution percentageStandard normal distribution and Z-scores
The resolution time for customer support queries follows a normal distribution with mean 30 minutes and standard deviation 5 minutes. (a) What percentage of queries are resolved in less than 25 minutes? (b) What percentage are resolved between 25 and 35 minutes? μ=30,σ=5\mu = 30, \quad \sigma = 5μ=3
The resolution time for customer support queries follows a normal distribution with mean 30 minutes and standard deviation 5 minutes. (a) What percentage of queries are resolved in less than 25 minutes? (b) What percentage are resolved between 25 and 35 minutes? μ=30,σ=5\mu = 30, \quad \sigma = 5μ=30,σ=5[5]
- Mean: $\mu = 30$ minutes - Standard deviation: $\sigma = 5$ minutes - Distribution: Normal, $X \sim N(30, 5^2)$ --- Standardize using $Z = \dfrac{X - \mu}{\sigma}$: $$Z = \frac{25 - 30}{5} = \frac{-5}{5} = -1$$ Look up the cumulative probability: $$P(Z < -1) = 0.1587$$ Answer (a): Approximately...