Answer:
116.45 is the minimum score needed to be stronger than all but 5% of the population.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 100
Standard Deviation, σ = 10
We are given that the distribution of score is a bell shaped distribution that is a normal distribution.
Formula:
![z_{score} = \displaystyle\frac{x-\mu}{\sigma}](https://tex.z-dn.net/?f=z_%7Bscore%7D%20%3D%20%5Cdisplaystyle%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D)
We have to find the value of x such that the probability is 0.05
P(X > x)
Calculation the value from standard normal z table, we have,
![P(z](https://tex.z-dn.net/?f=P%28z%3C1.645%29%20%3D%200.95)
Hence, 116.45 is the minimum score needed to be stronger than all but 5% of the population.