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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

Sagot :

Step 1: Write out the Z score formula

[tex]\begin{gathered} Z=\frac{x-\mu}{\sigma} \\ x=\text{score} \\ \mu=\operatorname{mean} \\ \sigma=s\tan dard\text{ deviation} \end{gathered}[/tex]

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

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

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
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