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Scores on an exam follow an approximately normal distribution with a mean of 76. 4 and a standard deviation of 6. 1 points. What is the minimum score you would need to be in the top 5%?.

Answer :

The minimum Score you would need to be in the top 5% is;

86.4345

Approximate normal distribution

If someone is in the top 5%, 95% of the people are below them. We have to find the value x such that; P(X ≤ X) = 0.95

Now, the z-score that corresponds to a probability of 0.95 on the normal distribution table is 1.645

The z-score formula is;

z = (x' - μ)/σ

we are given;

Population mean; μ = 76.4

Standard deviation; σ = 6.1

Thus;

1.645 = (x' - 76.4)/6.1

x' = (1.645 * 6.1) + 76.4

x' = 86.4345

Read more about Approximate Normal Distribution at; https://brainly.com/question/25800303

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