Mathematics, 01.10.2019 21:30 kimjooin02

In a research sample of high school students, the variable “number of instagram followers” formed normal distribution with a mean of 45 and a standard deviation of 16. if the research sample contained 500 students, approximately how many had 21 or fewer friends?
a)7
b)467
c)21
d)33

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Answer from: djs1002

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 $\mu$ and standard deviation $\sigma$ , the z-score 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, which is the percentile of measure X.

In this problem:

Mean of 45, thus $\mu = 41$ .Standard deviation of 16, thus $\sigma = 16$ .The proportion with 21 or fewer followers is the p-value of Z when X = 21, thus:

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

$Z = \frac{21 - 45}{16}$

Z = -1.5

Z = -1.5 has a p-value of 0.0668.

Out of 500 students:

0.0668(500) = 33

Approximately 33 students, option D.

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