Question

# Problem 7 Suppose you have a random variable X that represents the lifetime of a certain...

Problem 7

Suppose you have a random variable X that represents the lifetime of a certain brand of light bulbs. Assume that the lifetime of light bulbs are approximately normally distributed with mean 1400 and standard deviation 200 (in other words X ~ N(1400, 2002)).

Answer the following using the standard normal distribution table:

Approximate the probability of a light bulb lasting less than 1250 hours.

Approximate the probability that a light bulb lasts between 1360 to 1460 hours.

Approximate the probability that a light bulb lasts more than 1500 hours.

Draw this distribution’s shape. Note the value of X that is in the middle of the distribution and use the empirical rule to approximate the values that contain the middle 68% and 95% of all observations.

Find the five-number summary of light bulb lifetimes (approximate A- and A+ by finding the outlier criteria based on the z-scores of the quantiles).

f) What is the probability that 225 randomly selected lightbulbs will have an average within 25 hours to the actual population mean?