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nalin [4]
3 years ago
15

Suppose a certain species of fawns between 1 and 5 months old have a body weight that is approximately normally distributed with

mean kilograms and standard deviation kilograms. Let x be the weight of a fawn in kilograms. Convert the following z interval to a x interval.
Mathematics
1 answer:
worty [1.4K]3 years ago
7 0

Answer:

z

Step-by-step explanation:

Assuming this complete question:

"Suppose a certain species of fawns between 1 and 5 months old have a body weight that is approximately normally distributed with mean \mu =26 kilograms and standard deviation \sigma=4.2 kilograms. Let x be the weight of a fawn in kilograms. Convert the following z interval to a x interval.

X"

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:

X \sim N(26,4.2)  

Where \mu=26 and \sigma=4.2

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

We know that the Z scale and the normal distribution are equivalent since the Z scales is a linear transformation of the normal distribution.

We can convert the corresponding z score for x=42.6 like this:

z=\frac{42.6-26}{4.2}=3.95

So then the corresponding z scale would be:

z

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