Question

The average score of golfers competing in the ACME INC Tournament is 71.5. In golf, the goal is to get the lowest score. A golfer knows he needs to be scored at least 20th percentile (a score at the bottom 20%) in order to qualify for the next round of the tournament. If the standard deviation of the golf scores is 3.12, he needs to score below what value in order to advance to the next round?

Answer 1

He needs to score below 68.88 in order to advance to the next round

Explanation:

Z-score

In a set with mean
`\mu` and standard deviation
`\sigma`, the zscore of a measure X is given by:

`Z = (X - \mu)/(\sigma)`

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

`\mu = 71.5, \sigma = 3.12`

He needs to score below what value in order to advance to the next round?

Below the 20th percentile, so below the value of X when Z has a pvalue of 0.20. So it is X when
`Z = -0.84`

`Z = (X - \mu)/(\sigma)`

`-0.84 = (X - 71.5)/(3.12)`

`X - 71.5 = -0.84*3.12`

`X = 68.88`

He needs to score below 68.88 in order to advance to the next round