Respuesta :
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:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
We have to find the value of x such that the probability is 0.05
P(X > x)
[tex]P( X > x) = P( z > \displaystyle\frac{x - 100}{10})=0.05[/tex]
[tex]= 1 -P( z \leq \displaystyle\frac{x - 100}{10})=0.05[/tex]
[tex]=P( z \leq \displaystyle\frac{x - 100}{10})=0.95 [/tex]
Calculation the value from standard normal z table, we have,
[tex]P(z<1.645) = 0.95[/tex]
[tex]\displaystyle\frac{x - 100}{10} = 1.645\\x =116.45[/tex]
Hence, 116.45 is the minimum score needed to be stronger than all but 5% of the population.
