Question

The life of a manufacturer's compact fluorescent light bulbs is normal, with mean 12,000 hours and standard deviation 2,000 hours. Seth wants to find the probability that a light bulb he purchased from this manufacturer will last no more than 14,500 hours.
How many standard deviations above the mean is 14,500 hours?

Answer 1

Mean = 12000
Standard Deviation = 2000

We have to find how many standard deviations is 14,500 away from the mean.
This can be achieved by calculating the z-score

Z-score tells us how many standard deviations above or below is a sample value from the mean. A positive z value shows, sample value is above the mean.

z score can be calculated as = (Sample Value - Mean )/Standard Deviation)
So,
Z-score = $\frac{14500-12000}{2000} =1.25$

This means, 14,500 is 1.25 standard deviations above the mean value 12,000.

Answer 2

The first question: "How many standard deviations above the mean is 14,500 hours?"

Answer: A. 1.25

The second question: "Using the standard normal table, the probability that Seth’s light bulb will last no more than 14,500 (P(z ≤ 1.25)) hours is about___."

Answer: 89%