MATH 1040 - Introduction to Statistics

Answer to Practice Problem 2

A factory produces light bulbs with a mean lifetime of 1,200 hours and a standard deviation of 100 hours. A quality control engineer selects a random sample of 36 bulbs.

  1. What is the probability that the lifetime of a single bulb is greater than 1,225 hours?
    • The probability is found by finding the area of the right tail of a standardized normal distribution using a Z-Table or a calculator
      • On a Z-Table,
        • The z-score is $z = \frac{1225 - 1200}{100} = \frac{25}{100} = 0.25
        • Look at the area left of z = 0.25
          • $P(z < 0.25) = 0.599$
        • Take the compliment to get the area to the right of z = 0.25
          • $P(z > 0.25) = 1 - P(z < 0.25) = 1 - 0.599 = 0.401$
      • On a TI-83/84, DISTR –> 2:normalcdf(
        • 2:normalcdf(1225,9999,1200,100) if using the values from the problem
        • 2:normalcdf(0.25,9999,0,1) if using the z-score (gives the same answer)
    • Probability = 0.401 = 40.1%

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