Question

1. cameron took 4 tests, and his scores were as follows: 100, 60, 80, and 30. cameron took another test that was scored x. the mean score of the 5 tests he took is 72. what is the value of x? a. 54 b. 67.5 c. 68.4 d. 90

Explanation:

Step1: Recall the formula for the mean

The formula for the mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\), where \(n\) is the number of data - points and \(\sum_{i = 1}^{n}x_{i}\) is the sum of the data - points. Here, \(n = 5\) and \(\bar{x}=72\). So, \(\sum_{i = 1}^{5}x_{i}=n\times\bar{x}=5\times72 = 360\).

Step2: Find the sum of the first four scores

The sum of the first four scores is \(100 + 60+80 + 30=(100 + 60)+(80 + 30)=160+110 = 270\).

Step3: Solve for \(x\)

We know that \(\sum_{i = 1}^{5}x_{i}=270 + x\). Since \(\sum_{i = 1}^{5}x_{i}=360\), then \(270+x=360\). Subtracting 270 from both sides gives \(x=360 - 270=90\).

Answer:

D. 90