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The standard deviation of a normal random variable x is $20. given that p(x ≤ $10) = 0.1841. from this we can determine that the mean of the distribution is equal to

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LammettHash
Let [tex]\mu[/tex] be the mean of [tex]X[/tex]. Then

[tex]\mathbb P(X\le10)=0.1841\iff\mathbb P\left(\underbrace{\dfrac{X-\mu}{20}}_Z\le\dfrac{10-\mu}{20}\right)=0.1841[/tex]

For a random variable [tex]Z[/tex] following the standard normal distribution, we have

[tex]\mathbb P(Z\le z)=0.1841\implies z\approx-0.8999[/tex]

Transform the random variable to get this critical value in terms of [tex]\mu[/tex]:

[tex]\dfrac{10-\mu}{20}=-0.8999\implies\mu\approx27.997[/tex]

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