Question

A normal distribution has a mean of 80.6 and a standard deviation of 13.9. Find the value where the lowest 5% of data ends.

Answer 1

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:

$P(X$

Compute the value of x as follows:

$P(\frac{X-\mu}{\sigma}$

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:

$z=\frac{x-\mu}{\sigma} \\-1.645=\frac{x-80.6}{13.9} \\x=80.6-(1.645\times13.9)\\=57.7345\\\approx57.73$

Thus, the lowest 5% of data ends at 57.73.