Distribution if the IQ

Assume that the IQ in the population follows a normal distribution with a mean of 100 points and a standard deviation of 10 points. With what probability among 15 randomly selected people:
a. Is there anyone with an IQ above 130 points?
b. Are there at least 2 people with an IQ above 130 points?

Correct answer:

a =  0.9807

Step-by-step explanation:

$$\begin{gathered} \mu =100 \\ \sigma =10 \\ n=15 \\ {p}_1=N(x<130,\mu ,\sigma ) \\ {p}_1=0.9987 \\ a=\left(\genfrac{}{}{0ex}{}{n}{n}\right)\cdot p_1^n\cdot (1-p_1{)}^{n-n}=(\genfrac{}{}{0ex}{}{15}{15})\cdot 0.9987^{15}\cdot (1-0.9987{)}^{15-15}=1\cdot 0.9987^{15}\cdot 0.0013^0=0.9807 \end{gathered}$$

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