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Reto Aebersold · Answer 1 · 2023-05-25T03:31:09+0000

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

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