Question

the ability to determine the age of some individuals can be difficult if there are not quality government records of birth. bone growth takes place at the growth plates at the end of long bones. once all growth plates fuse, growth stops, and an individual is considered a biological adult. the age at which growth plates fuse for males is approximately normally distributed with a mean of 19.4 years and a standard deviation of 16.3 months. complete parts (a) through (d). (a) what is the probability a males growth plates fuse after age 20? the probability a males growth plates fuse after age 20 is (round to four decimal places as needed.)

Explanation:

Step1: Convert units

Since the mean is in years and standard deviation is in months, convert \(20\) years to months. \(20\times12 = 240\) months, and \(\mu=19.4\times12=232.8\) months, \(\sigma = 16.3\) months.

Step2: Calculate the z - score

The formula for the z - score is \(z=\frac{x-\mu}{\sigma}\). Substitute \(x = 240\), \(\mu=232.8\), and \(\sigma = 16.3\) into the formula:
\(z=\frac{240 - 232.8}{16.3}=\frac{7.2}{16.3}\approx0.44\)

Step3: Find the probability

We want to find \(P(X>240)\), which is equivalent to \(P(Z>0.44)\). Since \(P(Z > z)=1 - P(Z\leq z)\), and from the standard normal table \(P(Z\leq0.44)=0.6700\)
\(P(Z>0.44)=1 - 0.6700=0.3300\)

Answer:

\(0.3300\)