Answer:
19.74% of temperatures are between 12.9°C and 14.9°C
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 question, we have that:
[tex]\mu = 16.3, \sigma = 2[/tex]
What proportion of temperatures are between 12.9°C and 14.9°C?
This is the pvalue of Z when X = 14.9 subtracted by the pvalue of Z when X = 12.9.
X = 14.9
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{14.9 - 16.3}{2}[/tex]
[tex]Z = -0.7[/tex]
[tex]Z = -0.7[/tex] has a pvalue of 0.2420
X = 12.9
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{12.9 - 16.3}{2}[/tex]
[tex]Z = -1.7[/tex]
[tex]Z = -1.7[/tex] has a pvalue of 0.0446
0.2420 - 0.0446 = 0.1974
19.74% of temperatures are between 12.9°C and 14.9°C