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Posted by on Sunday, January 22, 2012 at 4:14pm.

Shown below are the data giving the length of life of lights in an underground tunnel.

9.0 months 7.0 months
8.2 months 8.3 months
7.8 months 8.1 months
7.5 months 7.6 months
9.1 months 7.4 months

I calculated the standard deviation to be about 0.679.
Estimate the probability that a random chosen light will last as long as 7 months after installation. Assume the data to be described by a normal distribution.

Can anyone help me with the process I would use to calculate the answer? Thanks!

  • Statistics - , Sunday, January 22, 2012 at 7:31pm

    Use z-scores. Find the mean. You have already calculated standard deviation.

    Formula for z-scores is the following:
    z = (x - mean)/sd

    Use 7 for x. Calculate z-score. Determine the probability using a z-distribution table.

  • Statistics - , Sunday, January 22, 2012 at 7:42pm

    Thanks for the insight!

    So I've calculated the z-score to be about -1.47, or about -1.5. Looking at a z-distribution table, I see on the left a column for z-scores and I see -1.5 there, but there are many values corresponding on the right?

    Do you know how I know which one to use?

  • Statistics - , Sunday, January 22, 2012 at 7:58pm

    Never mind- I've figured it out, THANK YOU MathGuru!

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