Respuesta :
Using the normal distribution, it is found that approximately 33 students had 21 or fewer friends, given by option D.
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In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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, which is the percentile of measure X.
In this problem:
- Mean of 45, thus [tex]\mu = 41[/tex].
- Standard deviation of 16, thus [tex]\sigma = 16[/tex].
- The proportion with 21 or fewer followers is the p-value of Z when X = 21, thus:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{21 - 45}{16}[/tex]
[tex]Z = -1.5[/tex]
[tex]Z = -1.5[/tex] has a p-value of 0.0668.
Out of 500 students:
[tex]0.0668(500) = 33[/tex]
Approximately 33 students, option D.
A similar problem is given at https://brainly.com/question/13383035
