The mean and standard deviation of the grades of 500 students who took a statistics test were 69 and 7, respectively. The shape of the distribution is not known. Based on this information, which one of the following is the best estimate of the percentage of students with grades between 55 and 83?

To determine the best estimate of the percentage of students with grades between 55 and 83, we can make use of the empirical rule, commonly known as the 68-95-99.7 rule, which applies to normal distributions. Although the shape of the distribution is not explicitly stated, many real-world datasets tend to follow a normal distribution closely enough that we can use this rule as a guide.

First, we calculate how many standard deviations away the grades of 55 and 83 are from the mean of 69. The standard deviation is 7.

For a score of 55:

• The difference from the mean (69) is 69 - 55 = 14.

• In terms of standard deviations, this is 14 / 7 = 2 standard deviations below the mean.

For a score of 83:

• The difference from the mean (69) is 83 - 69 = 14.

• In terms of standard deviations, this is also 14 / 7 = 2 standard deviations above the mean.

According to the empirical rule, approximately 95% of the data lies within 2 standard deviations from the mean in a normal distribution. Therefore, we can estimate that approximately 95%