Question

A data set has a mean of 112 and a standard deviation of 2.5.

Answer 1

Answer with explanation:

Mean of the data set$\mu$ = 112

Standard Deviation of the data set$\sigma$ =2.5

Since , 50% of data lies on both side of the mean.

 Z at 50% = 0.1915

Margin of error for this data set

       $=Z_{50 \text{percent}}\times\frac{\sigma}{\sqrt{\mu}}\\\\=0.1915 \times \frac{2.5}{\sqrt{112}}\\\\=0.1915 \times \frac{2.5}{10.58}\\\\=0.1915 \times 0.2362\\\\=0.0452$    

Margin of error=0.045(approx)

Answer 2

Answer:

The margin of error for this data set is option B )5

Step-by-step explanation:

Given that a data set has a mean of 112 and a std deviation of 2.5

Since confidence interval level is not given, we can take it as 95% normally used much in finding margin of errors.

For 95% confidence interval, Z critical value is 1.96 or approximately 2.

Margin of error = Z critical * std deviation

= 2(2.5)

=5

Hence option B would b the right answer

The margin of error for this data set is option B )5