Answer :
Answer:
The lowest 5% of data ends at 57.73.
Step-by-step explanation:
Let the random variable X follow a Normal distribution with mean μ = 80.6 and standard deviation σ = 13.9.
The lowest 5% of the distribution can be expressed in terms of probability as follows:
[tex]P(X<x)=0.05[/tex]
Compute the value of x as follows:
[tex]P(\frac{X-\mu}{\sigma}<\frac{x-80.6}{13.9})=0.05\\P(Z<z)=0.05[/tex]
The z score such that P (Z < z) = 0.05 is z = -1.645.
**Use the z-table for the for the z-score.
The value of x is:
[tex]z=\frac{x-\mu}{\sigma} \\-1.645=\frac{x-80.6}{13.9} \\x=80.6-(1.645\times13.9)\\=57.7345\\\approx57.73[/tex]
Thus, the lowest 5% of data ends at 57.73.
