We know that the percentage amount of any number can be found by first converting the the given percentage to a fraction and then multiplying it by the given number. Thus, in our case, the exact value, that is 48% of 1165 can be calculated as follows:
We know that
Therefore, 48% of 1165 can be re-written as:
This can be calculated as [tex]0.48\times 1165=559.2[/tex
Therefore The exact value that is 48% of 1165 is 559.2
Answer:
a) 68% of the men fall between 169 cm and 183 cm of height.
b) 95% of the men will fall between 162 cm and 190 cm.
c) It is unusual for a man to be more than 197 cm tall.
Step-by-step explanation:
The 68-95-99.5 empirical rule can be used to solve this problem.
This values correspond to the percentage of data that falls within in a band around the mean with two, four and six standard deviations of width.
<em>a) What is the approximate percentage of men between 169 and 183 cm? </em>
To calculate this in an empirical way, we compare the values of this interval with the mean and the standard deviation and can be seen that this interval is one-standard deviation around the mean:
Empirically, for bell-shaped distributions and approximately normal, it can be said that 68% of the men fall between 169 cm and 183 cm of height.
<em>b) Between which 2 heights would 95% of men fall?</em>
This corresponds to ±2 standard deviations off the mean.
95% of the men will fall between 162 cm and 190 cm.
<em>c) Is it unusual for a man to be more than 197 cm tall?</em>
The number of standard deviations of distance from the mean is
The percentage that lies outside 3 sigmas is 0.5%, so only 0.25% is expected to be 197 cm.
It can be said that is unusual for a man to be more than 197 cm tall.