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frozen [14]
3 years ago
10

a baseball team scored the following number of runs in its game this season: 6, 2, 5, 9, 11, 4, 5, 8, 6, 7, 5. there is one more

game in the season. if the team wants to end the season with an average of at least 6 runs per game, what us the least number of runs the team must score in the final game of the season?
Mathematics
1 answer:
frez [133]3 years ago
7 0
After the season, 12 games would be played, and you need to know this to work out the mean
Let's call the number of points needed for a 6 point average 'x'
The mean would be: 6 + 2 + 5 + 9 + 11 + 4 + 5 + 8 + 6 + 7 + 5 + x = 12 * 6
Simply put:
68 + x = 72
Then simplify it
x = 4
They would need 4 points to end the season with an average of 6 points

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If the distribution is really (5.43,0.54)
defon

Answer:

0.7486 = 74.86% observations would be less than 5.79

Step-by-step explanation:

I suppose there was a small typing mistake, so i am going to use the distribution as N (5.43,0.54)

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

The general format of the normal distribution is:

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Which means that:

\mu = 5.43, \sigma = 0.54

What proportion of observations would be less than 5.79?

This is the pvalue of Z when X = 5.79. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{5.79 - 5.43}{0.54}

Z = 0.67

Z = 0.67 has a pvalue of 0.7486

0.7486 = 74.86% observations would be less than 5.79

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