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3 years ago

11

The expression means 15 minus the product of 5 times the difference of p minus 6. If p = 8, then the value of the expression is

.

1 answer:

MA_775_DIABLO [31]3 years ago

3 0

Answer:

5

Step-by-step explanation:

from the question:

15-5(p-6)

when p=8,

=15-5(8-6)

=15-5(2)

=15-10

=5

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Step-by-step explanation:

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Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

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The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

$\mu = 200, \sigma = 50, n = 100, s = \frac{50}{\sqrt{100}} = 5$

a. What is the probability that the sample mean will be within +/- 5 of the population mean (to 4 decimals)?

This is the pvalue of Z when X = 200 + 5 = 205 subtracted by the pvalue of Z when X = 200 - 5 = 195.

Due to the Central Limit Theorem, Z is:

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

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

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

$Z = \frac{195 - 200}{5}$

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$Z = -1$ has a pvalue of 0.1587.

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b. What is the probability that the sample mean will be within +/- 10 of the population mean (to 4 decimals)?

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$Z = \frac{210 - 200}{5}$

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$Z = -2$ has a pvalue of 0.0228.

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