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ira [324]
3 years ago
11

The average maximum monthly temperature in Campinas, Brazil is 29.9 degrees Celsius. The standard deviation in maximum monthly t

emperature is 2.31 degrees. Assume that maximum monthly temperatures in Campinas are normally distributed. What percentage of months would have a maximum temperature of 32 degrees or higher? Round your answer to one decimal place.
Mathematics
1 answer:
kvv77 [185]3 years ago
8 0

Answer:

P(X>32)=P(\frac{X-\mu}{\sigma}>\frac{32-\mu}{\sigma})=P(Z>\frac{32-29.9}{2.31})=P(z>0.909)

And we can find this probability with the complement rule and using the normal standard distributon table or excel we got:

P(z>0.909)=1-P(z

And if we convert this to a % we got 18.2 % of maximum temperatures higher or equal than 32 C

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 maximum monthly temperature of a population, and for this case we know the distribution for X is given by:

X \sim N(29.9,2.31)  

Where \mu=29.9 and \sigma=2.31

We are interested on this probability

P(X>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(X>32)=P(\frac{X-\mu}{\sigma}>\frac{32-\mu}{\sigma})=P(Z>\frac{32-29.9}{2.31})=P(z>0.909)

And we can find this probability with the complement rule and using the normal standard distributon table or excel we got:

P(z>0.909)=1-P(z

And if we convert this to a % we got 18.2 % of maximum temperatures higher or equal than 32 C

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