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andrew-mc [135]
3 years ago
12

Heights of men on a basketball team have a bell shaped distribution with a mean of 173 cm and a standard deviation of 8 cm using

the empirical rule what is the approximate percentage of the men between the following
a. 165 cm and 181 cm
b. 149 cm and 197cm
Mathematics
2 answers:
telo118 [61]3 years ago
6 0

Answer:

a. 68%

b. 99.7%                

Step-by-step explanation:

Bell-shaped distribution means Normal distribution.

For finding the percentage first we have to calculate the value of: \frac{x-\bar x}{\sigma}

If its value is ±1, then using empirical formula percentage = 68%

If its value is ±2, then using empirical formula percentage = 95%

and, If its value is ±3, then using empirical formula percentage = 99.7%

a. \frac{165 - 173}{8} = -1 \ \ and \ \ \frac{181 - 173}{8} = 1

Thus, 68% of data lie within 1 standard deviation of the mean.

b. \frac{149 - 173}{8} = -3 \ \ and \ \ \frac{197 - 173}{8} = 3

Thus, 99.7% of data lie within 3 standard deviation of the mean.

ASHA 777 [7]3 years ago
3 0
I have a similar problem here with a slightly different given. 

Heights of men on a baseball team have a bell shaped distrubtion with a mean of 172cm and a standard deviation of 7cm. Using that is the empirical rule, what is the approximate percentage of the men between the following values? 
a) 165 cm and 179cm 
<span>b) 151cm and 193cm
</span>
The solution is:

 <span>a. (165-172)/7 = -1, (179-172)/7 = 1, % by empirical rule = 68% 

b. (151-172)/7 = -3, (193-172)/7 = 3, % by empirical rule = 99.7%
</span>
I hope that by examining the solution for this problem, it could help you  answer your problem on your own.
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