Question

In a distribution with a mean of 100 and a standard deviation of 15, the probability that a score
will be 115 or higher is _____ Please show all your work.

Answer 1

Using the Zscore principle, the probability of obtaining a score which will be 115 or higher is 0.15866

Given the Parameters :

• Mean, μ = 100
• Standard deviation, σ = 15
• Score, X ≥ 115

Zscore = (X - μ) ÷ σ

Zscore = (115 - 100) ÷ 15

Zscore = 1

Using a normal distribution probability ;

P(Z ≥ 1) = 1 - P(Z ≤ 1)

P(Z ≥ 1) = 1 - 0.84134

P(Z ≥ 1) = 0.15866

Therefore, the probability is 0.15866

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