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prohojiy [21]
3 years ago
11

Costs for standard veterinary services at a local animal hospital follow a Normal distribution with a mean of $72 and a standard

deviation of $21. What is the probability that one bill for veterinary services costs between $32 and $111
Mathematics
1 answer:
Romashka [77]3 years ago
8 0

Answer:

P(32

And we can find this probability with this difference:

P(-1.905

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.  

P(-1.905

Step-by-step explanation:

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 costs of services of a population, and for this case we know the distribution for X is given by:

X \sim N(72,21)  

Where \mu=72 and \sigma=21

We are interested on this probability

P(32

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}

If we apply this formula to our probability we got this:

P(32

And we can find this probability with this difference:

P(-1.905

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.  

P(-1.905

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Because x is the placeholder for the amount of yes votes, and x = 3228, the amount of yes votes is 3228




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