Question

The average maximum monthly temperature in Campinas, Brazil is 29.9 degrees Celsius. The standard deviation in maximum monthly temperature is 2.31 degrees. Assume that maximum monthly temperatures in Campinas are normally distributed. What percentage of months would have a maximum temperature of 34 degrees or higher?

Answer 1

Answer:

3.84% of months would have a maximum temperature of 34 degrees or higher

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:

$\mu = 29.9, \sigma = 2.31$

What percentage of months would have a maximum temperature of 34 degrees or higher?

This is 1 subtracted by the pvalue of Z when X = 34. So

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

$Z = \frac{34 - 29.9}{2.31}$

$Z = 1.77$

$Z = 1.77$ has a pvalue of 0.9616

1 - 0.9616 = 0.0384

3.84% of months would have a maximum temperature of 34 degrees or higher