Respuesta :
Explanation:
Formula for the given probability is as follows.
[tex]P(z > \frac{x - \mu}{\sigma})[/tex] = 0.10
[tex]P(z > \frac{10.256 - \mu}{\sigma})[/tex] = 0.10
According to the normal table area we have,
P(z < 1.28) = 0.10
Hence, [tex]\frac{10.256 - \mu}{\sigma} = 1.28[/tex]
[tex]\mu = 10.256 - 1.28 \times \sigma[/tex] .......... (1)
Also, the given probability is as follows.
[tex]P(z < \frac{x - \mu}{\sigma})[/tex] = 0.05
[tex]P(z < \frac{9.671 - \mu}{\sigma})[/tex] = 0.05
Hence, [tex]\frac{9.671 - \mu}{\sigma} = -1.645[/tex]
[tex]\mu = 9.671 + 1.645 \times \sigma[/tex] ....... (2)
Now, substitute the value of [tex]\mu[/tex] from equation (1) into equation (2) as follows.
[tex]10.256 - 1.28 \times \sigma = 9.671 + 1.645 \times \sigma[/tex]
[tex]-2.925 \sigma = -0.585[/tex]
[tex]\sigma[/tex] = 0.2
Putting the value of [tex]\sigma[/tex] into equation (2) we will find the value of [tex]\mu[/tex] as follows.
[tex]\mu = 9.671 + 1.645 \times \sigma[/tex]
= [tex]9.671 + 1.645 \times 0.2[/tex]
= 10
Thus, we can conclude that the value of [tex]\sigma[/tex] is 0.2 and the value of [tex]\mu[/tex] is 10.
