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Votes received by Wayne is 112
<em><u>Solution:</u></em>
To find: votes received by Wayne
Let the vote received by Wayne be "x"
<em><u>Juan received 4 times as many votes as Wayne</u></em>
Therefore,
Juan votes = 4 times as many votes as Wayne
Juan votes = 4x ---- eqn 1
<em><u>Neal received twenty less votes than Juan</u></em>
Neal votes = twenty less votes than Juan
Neal votes = Juan votes - 20
Neal votes = 4x - 20 ---- eqn 2
<em><u>Kerry got half as many votes as Neal</u></em>
Kerry votes = half of neal votes
Kerry votes = ---- eqn 3
The total votes cast in the election was 1,202
Wayne votes + Juan votes + Neal votes + Kerry votes = 1202
Plug in eqn 1 , eqn 2, eqn 3
Therefore votes received by Wayne is 112
Where the variance is 0.32, the mean is 0.40, and there are provided sets of probabilities, the standard deviation will be 0.566.
<h3>What is standard deviation?</h3>The average degree of variability in your dataset is represented by the standard deviation. It reveals the average deviation of each statistic from the mean. In general, values with a high standard deviation are spread out from the mean, whereas those with a low standard deviation are grouped together close to the mean.
Here,
mean=0.4
variance=(Xn-mean)².P(x)n
=(0-0.4)²*(0.64)+(1-0.4)²*(0.32)+(2-0.4)²*0.04
variance=0.32
Standard deviation=√(variance)
=√0.32
=0.566
The standard deviation will be 0.566 where variance in 0.32 and mean is 0.40 and given sets of probability.
To know more about standard deviation,
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