(Solved): Can you show me the detailed steps of how to get the correct answer for Q9 7 ...

Can you show me the detailed steps of how to get the correct answer for Q9

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7. If four observations on \( X \) are selected randomly from this distribution, the probability that one of them takes on a value of 0 is equal to (a) \( 0.1536 \) (b) \( 0.2 \) (c) \( 0.4096 \) (d) \( 0.8 \) (e) \( 0.8484 \) 8. In a random sample of 100 observations from this distribution, the probability that the sum of these \( X \) values is less that 180 is closest to (a) \( 0.0256 \) (b) \( 0.1536 \) (c) \( 0.8 \) (d) \( 0.9744 \) (e) \( 0.9983 \) 9. Let \( Y=10-2 X^{2} \). The probability \( P(Y<0) \) is equal to (a) \( 0.2 \) (b) \( 0.4 \) (c) \( 0.5 \) (d) \( 0.6 \) (e) none of these