Mathematics, 14.02.2020 18:16, strodersage

If the mean of a normally distributed population is -10 with a standard deviation of 2, what is the likelihood of obtaining a value less than or equal to -7?

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answered: jadadugas4418

There is a 93.32% probability of obtaining a value less than or equal to -7.

Given that,

The mean of a normally distributed population is = $\mu$ = -10.

And standard deviation = $\sigma$ = 2

WE have to find,

The likelihood of obtaining a value less than or equal to -7.

According to the question,

In a set with mean and standard deviation , the z-score of a measure X is given by:

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

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 p value, we get the probability that the value of the measure is greater than X.

This is the p value of Z when X = -7.

Then,

$z = \frac{x-\mu}{\sigma} \\\\z = \frac{-7 - (-10)}{2}$

$z = \frac{3}{2} \\\\z = 1.5$

z= 1.5 has a p value of 0.9332.

Hence, there is a 93.32% probability of obtaining a value less than or equal to -7.

For more information about Mean and Deviation click the link given below.

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answered: haydjanggg6578

93.32% probability of obtaining a value less than or equal to -7.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

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

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

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.

In this problem, we have that:

$\mu = -10, \sigma = 2$