Answer:
The required probability is 0.0228
Step-by-step explanation:
Consider the provided information.
Mean of 100 and a standard deviation of 15. You enrolled in a class of 25 students.
Therefore, [tex]\mu =100,\sigma 15[/tex]
We want the probability that the class' average IQ exceeds 130
As we know: [tex]z=\frac{\bar x -\mu}{\sigma}[/tex]
Substitute the respective value as shown:
[tex]z=\frac{130 -100}{15}[/tex]
[tex]z=\frac{30}{15}[/tex]
[tex]z=2[/tex]
[tex]P(z>2)=1-P(z<2)[/tex]
Now by using z table:
[tex]P(x>130)=P(z>2)=1-0.9772 [/tex]
[tex]P(x>130)=0.0228 [/tex]
Hence, the required probability is 0.0228
