Question

Given the age ( M = 19.83, SD = 3.07) of participants attending a kickboxing class, please answer the following:

a. Between what values do 68% of the data lie? _______________

b. Between what values do 95% of the data lie? _______________

Answer 1

Solution:

We are given that: Age of participants attending a kickboxing class has mean of M = 19.83 and Standard deviation = SD = 3.07

that is:   and

According to Empirical rule: for bell shaped distribution :

1) 68% of the data falls within 1 standard deviation from mean
that is :  

2) 95% of the data falls within 2 standard deviation from mean
that is :

3) 99.7% of the data falls within 3 standard deviation from mean
that is :  

Part a) Between what values do 68% of the data lie?

We know that 68% of the data falls within 1 standard deviation from mean, thus

Find :

and

Thus 68% of the data lie between 16.76 and 22.90 values.

Part b) Between what values do 95% of the data lie?

We know that 95% of the data falls within 2 standard deviation from mean.

Thus find:

Thus 95% of the data lie between 13.69 and 25.97 values.