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The number of students in each of your high school classes is normally distributed with a mean of 25 and a standard deviation of 5. What is the probability that your English class next year has more than 30 students in it?



Answer :

Answer:

The probability = 0.1587

Step-by-step explanation:

We can find the probability that the English class next year has more than 30 students in it by using the Normal Distribution Probability:

First, find the Z-score by using this formula:

[tex]\boxed{Z=\frac{x-\mu}{\sigma} }[/tex]

where:

  • [tex]Z=\text{Z-score}[/tex]
  • [tex]x=\text{observed value}[/tex]
  • [tex]\mu=\text{mean}[/tex]
  • [tex]\sigma=\text{standard deviation}[/tex]

Given:

  • [tex]\mu=25[/tex]
  • [tex]sigma=5[/tex]
  • [tex]x=30[/tex]

Hence:

[tex]\begin{aligned}\\Z&=\frac{x-\mu}{\sigma}\\\\&=\frac{30-25}{5} \\\\&=1\end{aligned}[/tex]

Next, by using the Normal Distribution Table, we can find the probability of P(x > 30) = P(Z > 1). Based on the table:

[tex]\begin{aligned}P(Z \leq 1)&=0.8413\\P(Z > 1)&=1-P(Z\leq 1)\\P(x > 30)&=1-0.8413\\&=\bf 0.1587\end{aligned}[/tex]

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