Question

Suppose that in a bowling league, the scores among all bowlers are normally distributed with mean µ = 182 points and standard deviation σ = 14 points. A trophy is given to each player whose score is at or above the 97th percentile. What is the minimum score needed for a bowler to receive a trophy?

Answer 1

Answer:

209 points

Step-by-step explanation:

Mean points scored (μ) = 182 points  

Standard deviation (σ) = 14 points

The z-score for any given game score 'X' is defined as:  

$z=\frac{X-\mu}{\sigma}$  

At, the 97th percentile of a normal distribution, the z-score, according to a z-score table, is 1.881.

Therefore, the minimum score, X, needed for a bowler to receive a trophy is:

$1.881=\frac{X-182}{14}\\X=208.334$

Since only whole point scores are possible, X=209 points.