Question

Laboratory tests show that the lives oflight bulbs are normally distributed witha mean of 750 hours and a standarddeviation of 75 hours. Find theprobability that a randomly selectedlight bulb will last between 900 and 975hours.[? ]%

Answer 1

We know that

• The mean is 750 hours.

,

• The standard deviation is 75 hours.

To find the probability between 900 and 975, we have to find

$P(900Remember that these probabilities fall into a normal distribution, where we can construct the intervals using the mean and the standard deviation.

So, we have to find the z-score for p(900) and p(975).

[tex]Z_{900}=\frac{x-\mu}{\sigma}=\frac{900-750}{75}=\frac{150}{75}=2$$Z_{975}=\frac{x-\mu}{\sigma}=\frac{975-750}{75}=\frac{225}{75}=3$

Now, we use these values in the following

$P(900Where each probability is found using the z-scores table, there you find that each probability is [tex]\begin{gathered} P(z<3)=0.9986 \\ P(z<2)=0.9772 \end{gathered}$

We subtract

[tex]P(900To have it in percentage, we multiply by 100%[tex]P(900Therefore, the probability of selecting a light bulb that will last between 900 and 975 is 2.14%.