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A company announces that employees who scored in the top 15% on a performance test will be awarded an all expenses paid trip to HSW From past data, the scores on the performance test are known to be normally distributed with mean of 136 and standard deviation of 19. What score on the performance test would earn an employee a trip to Hawaii? Round your answer to the nearest whole number. a. 136 b. Not enough information is supplied to answer c. 160 d. 116 e. 156 f. 122

Answer :

Final answer:

Using statistical methods and understanding of the normal distribution, we find that an employee must score at least 157 on the performance test to be in the top 15% and earn a trip to Hawaii.

Explanation:

The subject at hand is a problem of statistics in mathematics. The idea is to find the threshold score that would place an employee in the top 15% of the performance. Because the scores are normally distributed, we can use the properties of the normal distribution to solve this problem.

First, we find the z-score corresponding to the top 15%. The z-score is a measure of how many standard deviations an element is from the mean. Looking up this z-score in a standard z-table, or using a calculator, we find that it is approximately 1.036.

Next, we use the following formula to calculate the score, X:
X = μ + z * σ
Where μ is the mean and σ is the standard deviation. Plugging in the known values, we find:
X = 136 + 1.036 * 19.

The answer is approximately 157, but round off to nearest whole number, so the score is 157. Therefore, an employee would need to score at least 157 on the performance test to go to Hawaii.

So the answer is (not in the options given).

Learn more about Normal Distribution here:

https://brainly.com/question/30390016

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