The Intelligence Quotient (IQ) test scores are normally distributed with a mean of 100 and a standard deviation of 15. You enrolled in a class of 25 students. What is the probability that the class' average IQ exceeds 130?

Answer:The required probability is 0.0228Step-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 130As 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