The lifetimes of a certain brand of photographic are normally distributed with a mean of 210 h and a standard deviation of 50 h. What percent of lights will need to be replaced within 235 h? Show Work

69.15% of lights will need to be replaced within 235 h.

Step-by-step explanation:

We are given that the lifetimes of a certain brand of photographic are normally distributed with a mean of 210 h and a standard deviation of 50 h.

Let X = the lifetimes of a certain brand of photographic

The z-score probability distribution for the normal distribution is given by;

                              Z  =    ~ N(0,1)

where, = population mean lifetime = 210 h

            = standard deviation = 50 h

Now, the percent of lights that will need to be replaced within 235 h is given by = P(X 235 h)

      P(X 235 h) = P( ) = P(Z 0.50) = 0.6915 or 69.15%

The above probability is calculated by looking at the value of x = 0.5 in the z table which has an area of 0.6915.

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