*Will give medal!*
The life expectancy of a typical lightbulb is normally distributed with a mean of 1,975 hours and a standard deviation of 25 hours. What is the probability that a lightbulb will last between 1,950 and 2,050 hours?

0.84

0.77

0.82

0.89

Question

*Will give medal!*
The life expectancy of a typical lightbulb is normally distributed with a mean of 1,975 hours and a standard deviation of 25 hours. What is the probability that a lightbulb will last between 1,950 and 2,050 hours?

 0.84

 0.77

 0.82

 0.89

anonymous · Answer

$$\begin{align*}P(1950<X<2050)&=P\left(\frac{1950-1975}{25}<\frac{X-1950}{25}<\frac{2050-1975}{25}\right)\
&=P(-1<Z<3)
\end{align*}$$

anonymous · Answer

Are you calculation the z score? Im confused @SithsAndGiggles

imstuck · Answer

Yes she is calculating the z score.  That's the only way to find the probability you need.

anonymous · Answer

Yeah, you transform for a normal distribution to the standard normal distribution with the formula
$$Z=\frac{X-\text{mean}}{\text{standard deviation}}$$

anonymous · Answer

Okay so the answer is between -1 and 3?

anonymous · Answer

The answer is a probability, between 0 and 1.

anonymous · Answer

So where do I go from here?

anonymous · Answer

Refer to a z-table for the probabilities, or use a calculator to compute it for you: http://www.wolframalpha.com/input/?i=P%28-1%3Cz%3C3%29

anonymous · Answer

Sop its .84?

anonymous · Answer

yes

anonymous · Answer

Thank you so much!