Question

a. find the mean and the standard deviation for the numbers of girls in groups of 30 births. the value of the mean is \\( \mu = 15 \\). (type an integer or a decimal. do not round.) the value of the standard deviation is \\( \sigma = 2.7 \\). (round to one decimal place as needed.) b. use the range rule of thumb to find the values separating results that are significantly low or significantly high. values of 9.6 girls or fewer are significantly low. (round to one decimal place as needed.) values of 20.4 girls or greater are significantly high. (round to one decimal place as needed.) c. is the result of 26 girls a result that is significantly high? what does it suggest about the effectiveness of the method? the result \\( \square \\) significantly high, because 26 girls is \\( \square \\) girls. a result of 26 girls would suggest that the method (round to one decimal place as needed.)

Explanation:

Step1: Calculate the range for significantly low values

The formula for significantly low values is \(\mu - 2\sigma\).
Given \(\mu = 15\) and \(\sigma=2.7\), we substitute these values into the formula:
\(15 - 2\times2.7=15 - 5.4 = 9.6\)

Step2: Calculate the range for significantly high values

The formula for significantly high values is \(\mu + 2\sigma\).
Substitute \(\mu = 15\) and \(\sigma = 2.7\) into the formula:
\(15+2\times2.7=15 + 5.4=20.4\)

Step3: Determine if 26 is significantly high

Since \(26>20.4\), 26 is significantly high. This suggests that the method is effective as it results in a number of girls (26) that is greater than the value (\(20.4\)) which separates significantly high results from non - significant ones.

Answer:

b. Significantly low: \(9.6\) girls; Significantly high: \(20.4\) girls
c. Yes, 26 girls is significantly high. It suggests that the method is effective.