a gymnastics coach records the scores of a gymnast and develops the probability distribution below. what is…
a gymnastics coach records the scores of a gymnast and develops the probability distribution below. what is the probability the gymnast scores a 9 or 9.5?\nprobability distribution\ngymnastics score: x\tprobability: p(x)\n5\t0.02\n5.5\t0.02\n6\t0.06\n6.5\t0.1\n7\t0.16\n7.5\t0.14\n8\t0.18\n8.5\t0.18\n9\t?\n9.5\t0.02
Answer
Explanation:
Step1: Recall probability - sum rule
The sum of all probabilities in a probability distribution is 1. First, find the sum of the given probabilities: $0.02 + 0.02+0.06 + 0.1+0.16+0.14+0.18+0.18+0.02=0.88$.
Step2: Calculate $P(9)$
Let $P(9)=x$. Since the sum of all probabilities is 1, we have $0.88 + x+0.02 = 1$. Solving for $x$, we get $x=1-(0.88 + 0.02)=0.1$.
Step3: Calculate $P(9\ or\ 9.5)$
Using the addition - rule for mutually - exclusive events $P(A\ or\ B)=P(A)+P(B)$. Here, $A$ is the event of scoring 9 and $B$ is the event of scoring 9.5. So $P(9\ or\ 9.5)=P(9)+P(9.5)$. Substitute $P(9) = 0.1$ and $P(9.5)=0.02$ into the formula: $P(9\ or\ 9.5)=0.1 + 0.02=0.12$.
Answer:
$0.12$