Answer :
Complete Question
Assume the random variable x is normally distributed with mean u=87 and standard deviation o=5. Find the indicated probability.
P(x<81)
P(x<81)=__(Round to four decimal places).
Answer:
The value is [tex]P(x < 81) = 0.11507[/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 87[/tex]
The standard deviation is [tex]\sigma = 5[/tex]
The probability is mathematically represented as
[tex]P(x < 81) = P (\frac{X - \mu }{\sigma } < \frac{81 - 87 }{5 } )[/tex]
Generally [tex]\frac{X - \mu}{\sigma} = Z (The \ z-score \ of X )[/tex]
[tex]P(x < 81) = P (Z < - 1.2)[/tex]
From the z-table
[tex]P (Z < - 1.2) = 0.11507[/tex]
So [tex]P(x < 81) = 0.11507[/tex]