Question

Brainliest + Points!

Does anyone know how to do this?

For the following data set, calculate the percentage of data points that fall within one standard deviation of the mean, and compare the result to the expected percentage of a normal distribution.

{55, 54, 66, 38, 53, 56, 57, 66, 45, 65}

A.
50%; This percentage is lower than expected in a normal distribution.

B.
60%; This percentage is lower than expected in a normal distribution.

C.
70%; This percentage is close to the expected percentage in a normal distribution.

D.
80%; This percentage is higher than expected in a normal distribution.

Answer 1

Answer:

A. 50%; This percentage is lower than expected in a normal distribution

Answer 2

Answer:

A) 50%; This percentage is lower than expected in a normal distribution.

Step-by-step explanation:

Data points given:

55, 54, 66, 38, 53, 56, 57, 66, 45, 65

n = 10

The mean for the data points:

$\frac{55+54+66+38+53+56+57+66+45+65}{10}$

Mean = 55.5

Standard deviation of data points:

$= \sqrt{\frac{55-55.5)^2+(54-55.5)^2+(66+55.5)^2+(38-55.5)^2+(53-55.5)^2+(56-55.5)^2+(57-55.5)^2+(66-55.5)^2+(45-55)^2+(65-55)^2}{10}}$

= 8.59

Now let's find the data points that lie between 64.09 i.e (55.5 + 8.59) and 46.91 i.e (55.5-8.59)

We can see that 5 data points lie between 64.09 and 46.91 which are { 55,54,53,56,57}

The correct option is A, which states that 50% percentage is lowee than expected.