Answer to Question #218503 in Statistics and Probability for Yasmin

Question #218503

Suppose x is a normally distributed random variable with μ=46 and σ=3. Find a value x0 of the random variable x that satisfies the following equations or statements.

a.​ 10% of the values of x are less than x0.

b.​ 80% of the values of x are less than x0.

c.​ 1% of the values of x are greater than x0.


1
Expert's answer
2021-07-19T05:43:41-0400

a. P(Z<z0)=0.1.P(Z<z_0)=0.1.

z0=1.28.z_0=-1.28.

x0463=1.28.\frac{x_0-46}{3}=-1.28.

x0=461.283=42.16.x_0=46-1.28*3=42.16.


b. P(Z<z0)=0.8.P(Z<z_0)=0.8.

z0=0.84.z_0=0.84.

x0463=0.84.\frac{x_0-46}{3}=0.84.

x0=46+0.843=48.52.x_0=46+0.84*3=48.52.


c. P(Z>z0)=0.01P(Z<z0)=0.99.P(Z>z_0)=0.01\to P(Z<z_0)=0.99.

z0=2.33.z_0=2.33.

x0463=2.33.\frac{x_0-46}{3}=2.33.

x0=46+2.333=52.99.x_0=46+2.33*3=52.99.


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