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Assume the random variable x is normally distributed with mean y = 90 and standard deviation o=5. Find the indicated probability.P(75

User Adam Colvin
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1 Answer

8 votes
8 votes

Step 1: Write out the Z score formula


\begin{gathered} Z=(x-\mu)/(\sigma) \\ x=\text{score} \\ \mu=\operatorname{mean} \\ \sigma=s\tan dard\text{ deviation} \end{gathered}

Step 2: Calculate the z scores for the two values ( 75 and 80 )


\begin{gathered} Z_1\Rightarrow z-\text{score for 75} \\ Z_2\Rightarrow z-\text{score for 80} \end{gathered}
\begin{gathered} Z_1=(75-90)/(5)=-(15)/(5)=-3 \\ Z_2=(80-90)/(5)=-(10)/(5)=-2 \end{gathered}

The probability that the mean is between 75 and 80 will be

[tex]Pr(-3Thus, the probability will be[tex]\begin{gathered} Pr(-3Hence, the indicated probability P(75
Assume the random variable x is normally distributed with mean y = 90 and standard-example-1
User Vbali
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