# Normal Distribution Help

1. Apr 8, 2012

### FeDeX_LaTeX

A woollen mill produces scarves. The mill has several machines each operated by a different person. Jane has recently started working at the mill and the supervisor wishes to check the lengths of the scarves Jane is producing. A random sample of 20 scarves is taken and the length, x cm, of each scarf is recorded. The results are summarised as:

∑x = 1428, ∑x² = 102286

The mill's owners require that 90% of scarves should be within 10 cm of the mean length.

Find the value of σ that would satisfy this condition.

I considered

$$P(|\overline{X}| < 10) = 0.9$$

but that didn't get me anywhere. And I tried confidence intervals with the t-distribution but that didn't work. Their answer is 6.079. How did they get it?

Their only line of working is "10 = 1.6449σ". I recognise that 1.6449 is the value of z for which P(Z > z) = 0.05, but I don't understand how they formed that equation.

Last edited: Apr 8, 2012
2. Apr 8, 2012

### FeDeX_LaTeX

Never mind, got it...