Answer:
The mean, μ is 2.5063 and
The standard deviation, σ = 2.0499 × 10⁻²
Step-by-step explanation:
Here we have
[tex]z = \frac{x- \mu}{\sigma}[/tex]
[tex]z \sigma ={x- \mu}{}[/tex] and
10% have length < 2.48 in while
5% have length > 2.54 in
and
From the z score table
Critical z at 10% to the left = -1.282
Critical z at 5% to the right = 1.645
Therefore, the equations become
-1.282σ = 2.48 - μ → μ -1.282σ = 2.48
1.645σ = 2.54 - μ → μ + 1.645σ = 2.54
Solving the above equations gives
The mean, μ = 2.5063 and
The standard deviation, σ = 2.0499 × 10⁻².
