Question

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

Answer 1

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

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 =
`(X-\mu)/(\sigma)` ~ N(0,1)

where,
`\mu` = population mean lifetime = 210 h

`\sigma` = standard deviation = 50 h

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

P(X
`\leq` 235 h) = P(
`(X-\mu)/(\sigma)`
`\leq`
`(235-210)/(50)` ) = P(Z
`\leq` 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.