normal distribuation

Question

Laboratory tests show that the lives of light bulbs are normally distributed with a mean of 750 hours and a standard deviation of 75 hours. Find the probability that a randomly selected light bulb will last between 600 and 750 hours.

Answer 1

Let's use the formula for z test: z = (x-μ)/σ, where μ is the mean and σ is the standard deviation.

At x=600, z = (600-750)/75 = -2. Looking at a z table that gives tail probabilities, we see that a z-score of -2 corresponds to a probability of 0.0228, so P(x<600) = 0.0228.

Do the same at x=750: z = (750-750)/75 = 0, and a z-score of 0 corresponds to a tail probability of 0.5, so

P(x < 750) = 0.5.

Now, the problem is asking for the probability that x is between 600 and 750. This means we should subtract P(x < 750) - P(x < 600) = 0.5 - 0.0228 = 0.4772. 0.4772 should be your final answer.

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Answer 2

Or simply see that this is in the range between 0 and 2 standard deviations, below the mean, and look at the graphs/charts that have (on 1 side of the mean) 0-1 std deviation at 34.1% and 1-2 std deviations at 13.6%, and add to get 47.7%