Respuesta :
Answer:
36.88% probability that her pulse rate is between 68 beats per minute and 80 beats per minute.
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 problem, we have that:
[tex]\mu = 74, \sigma = 12.5[/tex]
Between 68 beats per minute and 80 beats per minute.
pvalue of Z when X = 80 subtracted by the pvalue of Z when X = 68. So
X = 80
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{80 - 74}{12.5}[/tex]
[tex]Z = 0.48[/tex]
[tex]Z = 0.48[/tex] has a pvalue of 0.6844
X = 68
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{68 - 74}{12.5}[/tex]
[tex]Z = -0.48[/tex]
[tex]Z = -0.48[/tex] has a pvalue of 0.3156
0.6844 - 0.3156 = 0.3688
36.88% probability that her pulse rate is between 68 beats per minute and 80 beats per minute.
