The grades on the last math exam had a mean of 72%. assume the population of grades on math exams is known to be distributed normally, with a standard deviation of 5%. approximately what percent of students earn a score between 72% and 87%?

Approximately 50%.  

Step-by-step explanation:

We have been given that the grades on the last math exam are normally distributed and had a mean of 72% and a standard deviation of 5%.

To find the percent of students, who will earn a score between 72% and 87% we will use z-score formula.

, where,

,

,

,

.

Let us find z-score corresponding to sample score of 72%.

Let us find z-score for sample score 87%.

Let us find the probability of z-score between 0 and 3.

Since we now that probability between two z-scores can be found by subtracting the probability of smaller area from bigger area.

Upon substituting our given values in above formula we will get,

Using normal distribution table we will get,

Let us convert our given probability to percentage by multiplying 0.49865 by 100.

Therefore, approximately 50% of students will earn a score between 72% and 87%.

42

step-by-step explanation:

2.2°  

step-by-step explanation:

let θ = the angle of elevation.

tanθ =77/2020

tanθ = 0.038 12

      θ = tan⁻¹0.038 12

      θ = 2.2°