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 0.3300. (round to four decimal places as needed.) (b) what is the probability a males growth plates fuse before age 17? the probability a males growth plates fuse before age 17 is □. (round to four decimal places as needed.)

Explanation:

Step1: Standardize the value

First, convert the standard deviation from months to years. Since \(1\) year has \(12\) months, \(\sigma=\frac{16.3}{12}\approx1.3583\) years. The mean \(\mu = 19.4\) years. For \(x = 17\), the z - score is calculated using the formula \(z=\frac{x-\mu}{\sigma}\).

$$z=\frac{17 - 19.4}{1.3583}=\frac{- 2.4}{1.3583}\approx - 1.77$$

Step2: Find the probability

We want to find \(P(X\lt17)\), which is equivalent to \(P(Z\lt - 1.77)\). Using the standard normal distribution table (or a calculator with a normal - distribution function, e.g., in Excel: NORM.S.DIST(-1.77,TRUE)), we know that \(P(Z\lt - 1.77)=0.0384\)

Answer:

\(0.0384\)