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EugenSunic · Answer 1 · 2023-12-26T02:45:25+0000

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

$P(900Remember that these probabilities fall into a normal distribution, where we can construct the intervals using the mean and the standard deviation.<p>So, we have to find the z-score for p(900) and p(975).</p>[tex]Z_(900)=(x-\mu)/(\sigma)=(900-750)/(75)=(150)/(75)=2$
$Z_(975)=(x-\mu)/(\sigma)=(975-750)/(75)=(225)/(75)=3$

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%.

Laboratory tests show that the lives oflight bulbs are normally distributed witha-example-1

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