# Problem 1 of 3

Ron wrote a History test and a Mathematics test. His scores, along with the mean and standard deviation for his class, are listed below. Assume that the class marks are normally distributed.

**Subject** | **Ron’s Score** | **Mean** | **Standard Deviation** |

History | 73 | 70 | 6.2 |

Mathematics | 67 | 64 | 5.3 |

(a) On which test did Ron perform better in relation to the class? Justify your answer.

(b) What percentage of the class scored between 65 and 75 on the History test?

(c) If the top 18% of the class received an A or a B on the History test, determine the minimum mark for a B.

**Solution**

**(a)** We find which test Ron had the greater z score on:

The formula to find the z score is **z=(x-µ)/ơ**

__History__: (73-70)/6.2 = **.483**

__Math__: (67-64)/5.3 = **.566**

So Ron did better on the Math test in relation to the class because the z score is greater.

**(b)**We find the z scores of 65 (low) and 75 (high).

Low: (65-70)/6.2 = **-.8**

High: (75-70)/6.2 = **.8**

Now that we have the z scores, we can use Shadenorm (shows graph) or Normalcdf (just shows percentage) to find the percentage of the class that scored between 65 and 75:

Normalcdf(-.8,.8) = .576 = **57.6%**

So 57.6% of the class scored between 65 - 75 on the history test.

**(c)**Here we use InvNorm. Since invnorm calculates the left side of the graph, we need to use the opposite (.82).

InvNorm(.82,70,6.2) = **75.67**

So 75.7% would be the minimum mark to get a B on the History test.

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