Answer:
The value is [tex]x = 74.416 \ in[/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 70.3\ in[/tex]
The standard deviation is [tex]\sigma = 2.1\ in[/tex]
Generally the probability of getting people with height in the top 2.5% is mathematically represented as
[tex]P(X > x ) = P(\frac{X - \mu }{\sigma} > \frac{x - 70.3 }{2.1 } ) = 0.025[/tex]
Generally
[tex]\frac{X - \mu }{\sigma} = Z (The \ standardized \ value \ of X )[/tex]
=> [tex]P(X > x ) = P(Z > \frac{x - 70.3 }{2.1 } ) = 0.025[/tex]
Generally the critical value of 0.025 from the normal distribution table is
[tex]Z_{0.025} = 1.96[/tex]
So
[tex]\frac{x - 70.3 }{2.1 } = 1.96[/tex]
=> [tex]x = 74.416 \ in[/tex]
The cut-off height will be "74.416 in".
This same probability of an occurrence occurring is defined by probability. There are several real-life scenarios in something we should forecast the result of such an occurrence.
According to the question,
Mean, μ = 70.3 in
Standard deviation, σ = 2.1 in
Now,
The probability of getting people with height be:
→ P(X > x) = P([tex]\frac{X -\mu}{\sigma} > \frac{x-70.3}{2.1}[/tex])
= 0.025
We know,
Z = [tex]\frac{X- \mu}{\sigma}[/tex]
→ P(X > x) = P(Z > [tex]\frac{x-70.3}{2.1}[/tex])
= 0.025
The critical value be:
[tex]Z_{0.025}[/tex] = 1.96
hence,
The cut-off height be:
[tex]\frac{x-70.3}{2.1}[/tex] = 1.96
x = 74.416 in
Thus the above answer is correct.
Find out more information about probability here:
https://brainly.com/question/24756209
