Question

Rhiannon made her first sky dive while in college. Based on a normal distribution with mean 52.8 years and standard deviation 10.3, what must the age of a skydiver be to fall in the bottom 11.12% of the distribution?

Answer 1

To fall in the bottom 11.12% of the distribution, the age of the skydiver must be approximately 39.41 years.

Step-by-step explanation:

To find the age of a skydiver that falls in the bottom 11.12% of the distribution, we first need to find the z-score corresponding to this percentile. The z-score can be found using the z-score formula: z = (x - mean) / standard deviation. Plugging in the given mean of 52.8 and standard deviation of 10.3, we solve for x as follows: z = (x - 52.8) / 10.3. Rearranging the formula, we get x = (z * 10.3) + 52.8. To find the z-score corresponding to the bottom 11.12% of the distribution, we look up the z-score in the z-table. The z-score corresponding to the bottom 11.12% is approximately -1.21. Plugging this value into the equation, we can find the age of the skydiver: x = (-1.21 * 10.3) + 52.8. Solving this equation, we find that the age of the skydiver must be approximately 39.41 years to fall in the bottom 11.12% of the distribution.