Question

A random sample of computer startup times has a sample mean of x¯=37.2 seconds, with a sample standard deviation of s=6.2 seconds. Since computer startup times are generally symmetric and bell-shaped, we can apply the Empirical Rule. Between what two times are approximately 95% of the data? Round your answer to the nearest tenth

Answer 1

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