PLEAS HELP ME OUT !!!!!!

Mathematics

1 answer:

Alecsey [184]3 years ago

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5. You can see it go up by 1

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A research study investigated differences between male and female students. Based on the study results, we can assume the popula

garri49 [273]

Using the normal distribution and the central limit theorem, it is found that the interval that contains 99.44% of the sample means for male students is (3.4, 3.6).

In a normal distribution with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

It measures how many standard deviations the measure is from the mean.

After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

In this problem:

The mean is of $\mu = 3.5$ .

The standard deviation is of $\sigma = 0.5$ .

Sample of 100, hence $n = 100, s = \frac{0.5}{\sqrt{100}} = 0.05$

The interval that contains 95.44% of the sample means for male students is between Z = -2 and Z = 2, as the subtraction of their p-values is 0.9544, hence:

Z = -2:

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$