Respuesta :
Answer:
a) 5.45%
b) 6.98%
Explanation:
We are given the following information in the question:
Mean, μ = 0.8%
Standard Deviation, σ = 2%
We are given that the distribution of profit is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
a) We have to find the value of x such that the probability is 0.99
P(X < x)
[tex]P( X < x) = P( z < \displaystyle\frac{x - 0.8}{2})=0.99[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(z < 2.326) = 0.99[/tex]
[tex]\displaystyle\frac{x - 0.8}{2} = 2.326\\\\x = 5.452 \approx 5.45[/tex]
Thus, 5.45% of assets does the company need to be 99% sure that it will have a positive equity at the end of the year.
b) We have to find the value of x such that the probability is 0.999
P(X < x)
[tex]P( X < x) = P( z < \displaystyle\frac{x - 0.8}{2})=0.999[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(z < 3.090) = 0.999[/tex]
[tex]\displaystyle\frac{x - 0.8}{2} = 3.090\\\\x = 6.98[/tex]
Thus, 6.98% of assets does the company need to be 99% sure that it will have a positive equity at the end of the year.
