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stepan [7]
3 years ago
14

Select the statements that describe a normal distribution.

Mathematics
1 answer:
Snezhnost [94]3 years ago
3 0

Answer: The statements that describe a normal distribution are;

a. The density curve is symmetric and bell-shaped.

b. The normal distribution is a continuous distribution.

Step-by-step explanation: The normal distribution is the most commonly used and important statistic tool. It is referred to as the "Bell Curve" because of its bell-shape and the the fact that it is symmetric density curve. A continuous distribution defines the possibilities of a continuous random variable and a prime example of a continuous distribution is the Normal distribution.

The normal distribution is not a discrete distribution because it does not have discrete variables. The normal distribution is not a flat line that extends from a minimum to a maximum but it is a continuous distribution that extends in a bell shape from one minimum value going up to a maximum value before descending back to another minimum value.

68% of a normal distribution curve falls with one standard deviation from the mean not 32%.

The two parameters that define a normal distribution is the mean and the standard deviation.

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A group of high school athletes has an average GPA of 2.7 with a standard deviation of 0.9. a)Find the percentage of athletes wh
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Answer:

a) The percentage of athletes whose GPA more than 1.665 is 87.49%.

b) John's GPA is 3.645.

Step-by-step explanation:

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.

In this problem, we have that:

\mu = 2.7, \sigma = 0.9

a)Find the percentage of athletes whose GPA more than 1.665.

This is 1 subtracted by the pvalue of Z when X = 1.665. So

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

Z = \frac{1.665 - 2.7}{0.9}

Z = -1.15

Z = -1.15 has a pvalue of 0.1251

1 - 0.1251 = 0.8749

The percentage of athletes whose GPA more than 1.665 is 87.49%.

b) John's GPA is more than 85.31 percent of the athletes in the study. Compute his GPA.

His GPA is X when Z has a pvalue of 0.8531. So it is X when Z = 1.05.

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

1.05 = \frac{X - 2.7}{0.9}

X - 2.7 = 1.05*0.9

X = 3.645

John's GPA is 3.645.

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