The Philips manufactures electric bulbs that have a length of life that is normally distributed with mean equal to 850 hours and standard deviation of 40 hours. Find the probability that a bulb burns between 780 and 834 hours.

[tex]z=\frac{x-\mu}{\sigma} \\\\where\ x\ is\ the\ raw\ score,\mu\ is\ the \ mean\ and\ \sigma\ is\ the\ standard\ deviation.\\\\Given\ that:\\\\mean(\mu)=850\ hours,\ standard\ deviation(\sigma)=40\ hours[/tex]

For x > 780 hours:

[tex]z=\frac{780-850}{40} \\\\z=-1.75[/tex]

For x < 834 hours:

[tex]z=\frac{834-850}{40} \\\\z=-0.4[/tex]

From the normal distribution table, P(780 < x < 834) = P(-1.75 < z < -0.4) = P(z < -0.4) - P(z < -1.75) = 0.3446 - 0.0401 = 0.3045 = 30.45%

The Philips manufactures electric bulbs that have a length of life that is normally distributed with mean equal to 850 hours and standard deviation of 40 hours. Find the probability that a bulb burns between 780 and 834 hours.​

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The Philips manufactures electric bulbs that have a length of life that is normally distributed with mean equal to 850 hours and standard deviation of 40 hours. Find the probability that a bulb burns between 780 and 834 hours.