Question

- Save & Exit Certify Lesson: 7.2 Central Limit Theorem with Me... KAYLA LOCKE Question 4 of 13, Step 1 of 1 2/13 Correct An operation manager at an electronics company wants to test their amplifiers. The design engineer claims they have a mean output of 482 watts with a variance of 121 What is the probability that the mean amplifier output would be greater than 479.4 watts in a sample of 59 amplifiers if the claim is true? Round your answer to four decimal places. Answer How to enter your answer Tables Keyp:

Answer 1

The central limit theorem states that if you have a population with mean μ and standard deviation σ and take sufficiently large random samples(usually n>=30) from the population with replacement, then the distribution of the sample means will be approximately normally distributed.

$If \quad X~\sim N(\mu,\sigma^2) \newline \frac{X-\mu}{\sigma} \sim N(0,1)$

Ans: mean output = 482 watts EM) variance - 121 (62) Mean het x be the mean output Using central limit thessen (defined above) TN N(MH, 6) *; X~ N(482, 1.4) el x > 479.4) .pl -482 > 479.4-482). P(Z > -1.8155) 1/759 1589 l 1- PC25-1.8155): 1-0.035P= 04550 - 0.9649