Answer:
0.148783124
Step-by-step explanation:
the probability that a randomly selected sixth-grade student reads less than 100 words per minute
P(X < 100)
= P(z < (100 - 125)/24))
= P(z < -1.0417) (from the z-table)
= 0.148783124
The probability that a randomly selected sixth-grade student reads less than 100 words per minute is 0.1492.
A z-table also known as the standard normal distribution table, helps us to know the percentage of values that are below (or to the left of the Distribution) a z-score in the standard normal distribution.
As it is given that the distribution is normal, with a mean of 125 words, while the standard deviation is 24 words. Therefore, the probability that a randomly selected sixth-grade student reads less than 100 words per minute can be written as,
[tex]P(X < 100)=P(z < \dfrac{100-\mu}{\sigma})[/tex]
[tex]=P(z < \dfrac{100-\mu}{\sigma})\\\\=P(z < \dfrac{100-125}{24})\\\\=P(z < -1.0416)\\\\=0.1492[/tex]
Hence, the probability that a randomly selected sixth-grade student reads less than 100 words per minute is 0.1492.
Learn more about Z-table:
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