and the the questions below given that the mean score in a math quiz is 50 standard deviation is 8 Round your answers in percent to the nearest hundredths (like .40346 is 40.35% Round your answers for of people to the nearest whole number (like 8.32 is 8)Do not use What is the area under the curve between 42 and 66? square What is the probability of having a value less than 58? square If there are 48 students who took the quiz, how many students scored greater than 66? square What is the area under the curve between 45 and 60? square If there are 30 students took the quiz, approximately how many students are expected to get less than 65? square

## Step 1: Calculate the z-scores for 42 and 66.### The z-score formula is , where is the value, is the mean, and is the standard deviation. For , . For , .## Step 2: Find the area between z = -1 and z = 2.### Using a z-table or calculator, the area to the left of is approximately 0.9772, and the area to the left of is approximately 0.1587. The area between these two z-scores is .## Step 3: Calculate the probability of a value less than 58.### The z-score for is . The area to the left of is approximately 0.8413.## Step 4: Calculate the number of students scoring greater than 66.### From Step 2, the area to the left of (corresponding to ) is 0.9772. The area to the right is . With 48 students, the number scoring greater than 66 is .## Step 5: Calculate the area under the curve between 45 and 60.### The z-score for is . The z-score for is . The area to the left of is approximately 0.8944, and the area to the left of is approximately 0.2660 (interpolating or using a calculator). The area between these z-scores is .## Step 6: Calculate the number of students scoring less than 65.### The z-score for is . The area to the left of is approximately 0.9696. With 30 students, the number scoring less than 65 is .