Let X be a continuous random variable with a normal distribution with a mean of 10 and a variance of 25. Suppose that you randomly picked 36 values for X and averaged these values together, calling this new random variable X. Find P(12X). Give your answer as a decimal rounded to four places (i.e. X.XXXX)

Respuesta :

Answer:

0.0082

Step-by-step explanation:

Data provided in the question:

Mean = 10

Variance = 25

Standard deviation = [tex]\sqrt{\text{variance}}

[tex]=\sqrt{25}=5 [/tex]

n=36

Given [tex]P(12 \leq \bar{x})[/tex]  

[tex]=P(\bar{x} \geq 12)[/tex]  

[tex]=P\left(\frac{\bar{x}-\mu_{x}}{\frac{\sigma}{\sqrt{n}}} \geq \frac{12-10}{\left(\frac{5}{\sqrt{36}}\right)}\right)[/tex]  

[tex]=P(z \geqslant 2 \cdot 4)[/tex]  

[tex]=1-P(z<2 \cdot 4)[/tex]  

By using z-table we get,

[tex]=1-0.9918[/tex]  

= 0.0082.

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