Question

How do you keep the answers on your profile for studying????

Answer 1

Given:

Number of sample (n) = 50

mean = 300

standard deviation (s) = 47

confidence level = 95%

The margin of error (MOE) can be calculated using the formula:

`\text{MOE = z }*\text{ }\frac{s}{\sqrt[]{n}}`

Where z is the z-score at the given confidence level

At 95% confidence level, the z-score is 1.960

The margin of error is thus:

`\begin{gathered} \text{MOE =1.96 }*\frac{47}{\sqrt[]{50}} \\ =\text{ 13.0277} \end{gathered}`

The formula to calculate the confidence interval is:

Where :

`\begin{gathered} \text{lower bound = mean - margin of error} \\ \text{upper bound = mean + margin of error} \end{gathered}`

Substituting:

`\begin{gathered} \text{lower bound = }300\text{ - 13.0277} \\ =\text{ 286.9723} \\ \approx\text{ 287} \\ \text{upper bound = 300 + 13.0277} \\ =\text{ 313.0277} \\ \approx\text{ 313} \end{gathered}`

Hence, if we to randomly sample from this population 100 times. The probability of having a score between 287 and 313 is 0.95