Question

light bulbs are measured in lumens​ (light output), watts​ (energy used), and hours​ (life). a standard white light bulb has a mean life of 675 hours and a standard deviation of 50 hours. a soft white light bulb has a mean life of 700 hours and a standard deviation of 35 hours. at a local science​ competition, both light bulbs lasted 750 hours. which light​ bulb's life span was​ better?

Answer 1

To compare the life spans of the two light bulbs that both lasted 750 hours, we calculate the z-score for each. The standard white light bulb had a z-score of 1.5, while the soft white had a z-score of approximately 1.43. The standard white's higher z-score indicates a lifespan that exceeded its expected duration by a larger margin, making it the better-performing light bulb.

Step-by-step explanation:

To determine which light bulb's life span was better when both lasted 750 hours, we compare their performance relative to their mean life and standard deviation.

For the standard white light bulb, with a mean life of 675 hours and standard deviation of 50 hours, the z-score is calculated as:

Z = (X - μ) / σ = (750 - 675) / 50 = 1.5,

Where X is the life span of the light bulb, μ is the mean, and σ is the standard deviation. For the soft white light bulb, with a mean life of 700 hours and standard deviation of 35 hours, the z-score is:

Z = (X - μ) / σ = (750 - 700) / 35 ≈ 1.43.

The bulb with the higher z-score lasted longer relative to its expected lifespan. Therefore, the standard white light bulb's life span was better because it had a higher z-score of 1.5 compared to the soft white's 1.43.

Answer 2

After calculating the number of standard deviations above the mean for both bulbs, the standard white light bulb was 1.5 standard deviations above its mean, compared to 1.43 for the soft white, making its 750-hour lifespan relatively better.

Step-by-step explanation:

To determine which light bulb's life span was better when both lasted 750 hours, we need to calculate how many standard deviations above the mean this is for each type of bulb.

For the standard white light bulb (mean = 675 hours, standard deviation = 50 hours):

(750 - 675) / 50 = 1.5 standard deviations above the mean

For the soft white light bulb (mean = 700 hours, standard deviation = 35 hours):

(750 - 700) / 35 ≈ 1.43 standard deviations above the mean

The standard white light bulb's life span was 1.5 standard deviations above its mean, which is a longer life span in terms of its own distribution than the soft white bulb, which was approximately 1.43 standard deviations above its mean. Thus, the standard white light bulb's life span was relatively better compared to its usual performance.