QuestionThe time required to assemble a single Play Station 3 is approximately normally distributed with $\mu=15.53$ minutes and $\sigma=1.6$ minutes. A random sample of 15 Play Station 3 assembly times is selected.
Find the minimum assembly time of the upper 10\% of average assembly times. $\square$

Studdy Solution
Calculate the minimum assembly time using the z-score:
$x = \mu + z \cdot \sigma_{\bar{x}} = 15.53 + 1.28 \cdot \frac{1.6}{\sqrt{15}}$
Calculate the value:
$x = 15.53 + 1.28 \cdot 0.413$
$x \approx 15.53 + 0.528 = 16.058$
The minimum assembly time of the upper 10% of average assembly times is approximately:
$\boxed{16.058 \text{ minutes}}$