Question

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)

Answer 1

0.0082

Explanation:

Data provided in the question:

Mean = 10

Variance = 25

Standard deviation =
`\sqrt{\text{variance}}</p><p>[tex]=√(25)=5`

n=36

Given
`P(12 \leq \bar{x})`

`=P(\bar{x} \geq 12)`

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

`=P(z \geqslant 2 \cdot 4)`

`=1-P(z<2 \cdot 4)`

By using z-table we get,

`=1-0.9918`

= 0.0082.