Question

Describe a normal probability distribution. a. bell-shaped.b. mean, median, and mode all equivalent.c. bimodal.d. symmetric around the mean.e. skewed to the right.f. models discrete random variables.g. most of the data fall within 3 standard deviations from the mean. h. uniform-shaped.

Answer 1

Answer:

a) bell-shaped.              

b) mean, median, and mode all equivalent.      

d) symmetric around the mean.        

g) most of the data fall within 3 standard deviations from the mean.

Step-by-step explanation:

We have to describe a normal distribution.

a. bell-shaped.

This is true a normal distribution is a bell shaped distribution.

b. mean, median, and mode all equivalent.

This is true for a normal distribution.

Mean = Mode = Median

c. Bimodal

The is not true about the normal distribution. A normal distribution is unimodal and the mode is equal to the mean of the distribution.

d. symmetric around the mean.

This is true. The normal distribution is centered around the mean

e. skewed to the right.

This is not a property of normal distribution.

f. models discrete random variables.

Normal distribution is a continuous distribution.

g. most of the data fall within 3 standard deviations from the mean.

This is true. According to Empirical rule, almost all the data lies within three standard deviation of mean.

h. uniform-shaped

This is not true. A normal distribution is bell shaped.

Answer 2

The options that properly describe a normal distribution are;

A) Bell Shaped

B) Mean, median and mode are equivalent

D) Symmetric about the mean

G) most of the data fall within 3 standard deviations from the mean

Some of the properties of normal distribution are that;

1. The mean, mode and median are all equal.
2. The curve is symmetric at the center around the mean. This implies a bell shaped curve.
3. Exactly half of the values are to the left of center and exactly half the values are to the right.
4. The total area under the curve is 1
5. It's a continuous distribution

Let us look at the options;

• A) this is correct from the properties listed above.
• B) This is also correct from the properties listed above.
• C) This is not true because the mode is equal to the median and the mean and thus can only be unimodal.
• D) This is true from the properties listed above.
• E) From property 3, this is wrong as it is not skewed to the right since it has half values to the left and half to the right.
• F) This is not true because normal distribution is continuous and not discrete.
• G) This is true based on the empirical rule of normal distribution because Empirical Rule states that 99.7% of data observed following a normal distribution lies within 3 standard deviations of the mean.
• H) Not true as from property 2 we can see that it is bell shaped.

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