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NemiM [27]
3 years ago
8

Suppose the scores on a test given to all juniors in a school district are normally distributed with a mean of 74 and a standard

deviation of 8. On a separate sheet of paper, draw a Normal Curve and label the mean, standard deviations, and the associated percentages.

Mathematics
1 answer:
ivann1987 [24]3 years ago
7 0

Answer:

\mu -\sigma = 66 , \mu +\sigma = 82

\mu -2\sigma = 58 , \mu +2\sigma = 90

\mu -3\sigma = 50 , \mu +3\sigma = 98

And in the figure attached we see the limits with the percentages associated.

Step-by-step explanation:

For this case we know that the random variable of interest is the scores on a test given to all juniors in a school district follows a normal distribution with the following parameters:

X \sim N(\mu= 74, \sigma =8)

For this case we know from the empirical rule that within one deviation from the mean we have approximately 68.2% of the data, within 2 deviations from the mean we have 95% and within 3 deviation 99.7%

We can find the limits and we got:

\mu -\sigma = 66 , \mu +\sigma = 82

\mu -2\sigma = 58 , \mu +2\sigma = 90

\mu -3\sigma = 50 , \mu +3\sigma = 98

And in the figure attached we see the limits with the percentages associated.

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