The mean score on a Math exam was 50% and the standard deviation was 10%. Assume the results were normally distributed.

(a) What percent of students earned a score between 50% and 70%?

(b) If 60 students took the exam, how many got a score between 50% and 70%?

Z = (x - μ)/SD

Z = (x -50)/10

a) Get the respective Z scores. Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion between the two Z scores.

b) Multiply the proportion above by 60.

To answer both parts of the question, you will need to use the properties of the normal distribution curve. The normal distribution is a continuous probability distribution that is symmetric and bell-shaped. It is characterized by its mean (μ) and standard deviation (σ).

(a) To find the percentage of students who earned a score between 50% and 70%, you first need to find the corresponding z-scores for these percentages. The z-score measures the number of standard deviations a particular value is from the mean.

To find the z-score for 50%, we subtract the mean from the value of interest and divide by the standard deviation:
z1 = (50% - 50%) / 10% = 0

Similarly, to find the z-score for 70%:
z2 = (70% - 50%) / 10% = 2

Next, you can use a z-table or calculator to find the area/probability between these two z-scores, which represents the percentage of students who scored between 50% and 70%.

(b) To determine the number of students who got a score between 50% and 70%, you would apply the same concept but now consider the actual number of students.

First, calculate the z-scores as done in part (a). Then multiply the percentage you found in part (a) by the total number of students (60) to get the number of students who fall within that range.

For example, if 30% of students scored between 50% and 70% based on part (a), you would multiply 0.30 by 60 to get the number of students in that range.

Note: It is always recommended to round the number of students to the nearest whole number since you cannot have a fraction of a student.

Please note that the above calculations assume a normal distribution, which might not be accurate if the sample size is small or if the population follows a different distribution.