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densk [106]
3 years ago
10

Let X be a continuous random variable with a normal distribution with a mean of 10 and a variance of 25. Suppose that you random

ly 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)
Mathematics
1 answer:
lora16 [44]3 years ago
5 0

Answer:

0.0082

Step-by-step explanation:

Data provided in the question:

Mean = 10

Variance = 25

Standard deviation = \sqrt{\text{variance}}[tex]=\sqrt{25}=5

n=36

Given P(12 \leq \bar{x})  

=P(\bar{x} \geq 12)  

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

=P(z \geqslant 2 \cdot 4)  

=1-P(z  

By using z-table we get,

=1-0.9918  

= 0.0082.

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