Question

Suppose a normally distributed set of data has a mean of 123 and a standard deviation of 15. Use the 68-95-99.7 rule to determine the percent of scores in the data set expected to be between the scores 108 and 153. Give your answer in decimal form (for example, enter 0.68, NOT 68 or 68%) and keep all decimal places throughout your calculations and in your final answer. g

Answer 1

Answer:

percent of scores in the data set  is 90.98%

Explanation:

Given data:

Mean = 123

standard deviation 15

Determine the percent of score between 108 to 153

P(108 < X < 153)

$= P(\frac{108 - 123}{11} < z < \frac{153-123}{11})$

$= P(-1.36 < z < 2.72)$

$= P(z < 2.72) - P(z < -1.36)$

[FROM STANDARD Z TABLE obtained the value of  z  

= 0.9967 - 0.0869 [FROM STANDARD Z TABLE]

= 0.9098

percent of scores in the data set  is 90.98%