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 18.7 years and a standard deviation of 15.3 months. Complete parts (a) through (d) below.

Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2).
(a) What is the probability a male's growth plates fuse after age 20 ?

The probability a male's growth plates fuse after age 20 is (Round to four decimal places as needed.)

Step 1 ：Given that the mean age at which growth plates fuse for males is 18.7 years and the standard deviation is 1.275 years, we are asked to find the probability that a male's growth plates fuse after age 20.

Step 2 ：We first need to calculate the z-score for age 20. The z-score is calculated using the formula \(Z = \frac{X - \mu}{\sigma}\), where \(X\) is the value we are interested in (in this case, 20 years), \(\mu\) is the mean, and \(\sigma\) is the standard deviation.

Step 3 ：Substituting the given values into the formula, we get \(Z = \frac{20 - 18.7}{1.275} = 1.0196078431372553\).

Step 4 ：The z-score tells us how many standard deviations our value is from the mean. In this case, 20 years is approximately 1.02 standard deviations above the mean.

Step 5 ：We then use the standard normal distribution table to find the probability that a score is greater than this z-score. The probability corresponding to a z-score of 1.02 is approximately 0.15395724189377558.

Step 6 ：Thus, the probability that a male's growth plates fuse after age 20 is approximately \(\boxed{0.1540}\).