Question

The age distribution of inmates on death row in Texas is approximately normal with mean 46.3 years and standard deviation 10.1 years. c. According to the​ normal-curve model, what percentage of​ death-row inmates are under 18 years of​ age?

Answer 1

To find the percentage of death-row inmates under 18 years of age in Texas, we can use the normal distribution with the given mean and standard deviation. By calculating the z-score for the age 18 and finding the proportion of the distribution to the left of the z-score, we can determine the percentage. The result is approximately 0.28%.

Step-by-step explanation:

To find the percentage of death-row inmates under 18 years of age, we need to determine the proportion of inmates whose age is less than 18 in the normal distribution with a mean of 46.3 years and a standard deviation of 10.1 years.

First, we calculate the z-score for the age 18 using the formula:

z = (x - μ) / σ

where x is the age, μ is the mean, and σ is the standard deviation. Plugging in the values, we have:

z = (18 - 46.3) / 10.1

Calculating this, we get:

z ≈ -2.801

Next, we can use a standard normal distribution table or a calculator to find the percentage of the distribution that falls to the left of this z-score. The closest value on the table for -2.801 is 0.0028. This represents the proportion of inmates on death row who are younger than 18 years of age. To convert this to a percentage, we multiply by 100:

Percentage ≈ 0.0028 * 100

Calculating this, we find that approximately 0.28% of death-row inmates in Texas are under 18 years of age.