Question

How do you find this answer on a TI-84 PLUS calculator?

The mean output of a certain type of amplifier is 498 watts with a standard deviation of 12 watts. f 86 amplifiers are sampled, what is the probability that the mean of the sample would differ from the population mean by less than 1.1 watts? Round your answer to four decimal places.

Answer 1

Given that, mean (μ) = 498 watts and

standard deviation $(\sigma)$ = 12 watts

sample size (n) = 86

We want to find, $P(|\bar x -\mu| < 1.1)$

$P(|\bar x -\mu| < 1.1) = P(-1.1 < \bar x -\mu < 1.1)$

Where,

$\bar x_1 = 498-1.1= 496.9$

$\bar x_2 = 498 + 1.1= 499.1$

That means, we want to find, $P(496.9 < \bar x < 499.1)$

Using TI-83 plus calculator we find this probability:

$=> P(496.9 < \bar x < 499.1) = 0.6047$

Therefore, required probability is 0.6047

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