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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
[tex]P(|\overline{X}| < 10) = 0.9[/tex]
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.
∑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
[tex]P(|\overline{X}| < 10) = 0.9[/tex]
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.
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