Answer:
95% of the data lies between 24.8 and 49.6
Step-by-step explanation:
* Lets revise the empirical rule
- The Empirical Rule states that almost all data lies within 3
standard deviations of the mean for a normal distribution.
- 68% of the data falls within one standard deviation.
- 95% of the data lies within two standard deviations.
- 99.7% of the data lies Within three standard deviations
- The empirical rule shows that
# 68% falls within the first standard deviation (µ ± σ)
# 95% within the first two standard deviations (µ ± 2σ)
# 99.7% within the first three standard deviations (µ ± 3σ).
* Lets solve the problem
- A random sample of computer startup times has a sample mean of
μ = 37.2 seconds
∴ μ = 37.2
- With a sample standard deviation of σ = 6.2 seconds
∴ σ = 6.2
- We need to find between what two times are approximately 95%
of the data
∵ 95% of the data lies within two standard deviations
∵ Two standard deviations (µ ± 2σ) are:
∵ (37.2 - 2 × 6.2) = 24.8
∵ (37.2 + 2 × 6.2) = 49.6
∴ 95% of the data lies between 24.8 and 49.6
* 95% of the data lies between 24.8 and 49.6
