Respuesta :

Answer:

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 [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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:

[tex]\mu = -10, \sigma = 2[/tex]

What is the likelihood of obtaining a value less than or equal to -7?

This is the pvalue of Z when X = -7.

So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{-7 -(-10)}{2}[/tex]

[tex]Z = \frac{3}{2}[/tex]

[tex]Z = 1.5[/tex]

[tex]Z = 1.5[/tex] has a pvalue of 0.9332.

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

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 = [tex]\mu[/tex]= -10.

And standard deviation = [tex]\sigma[/tex] = 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:

[tex]Z = \frac{x - \mu}{\sigma}[/tex]

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,

[tex]z = \frac{x-\mu}{\sigma} \\\\z = \frac{-7 - (-10)}{2}[/tex]

[tex]z = \frac{3}{2} \\\\z = 1.5[/tex]

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.

https://brainly.com/question/23044118