An english professor assigns letter grades on a test according to the following scheme. a: top 15% of scores b: scores below the top 15% and above the bottom 55% c: scores below the top 45% and above the bottom 19% d: scores below the top 81% and above the bottom 6% f: bottom 6% of scores scores on the test are normally distributed with a mean of 74.2 and a standard deviation of 9.6. find the numerical limits for a d grade. round your answers to the nearest whole number, if necessar

59 to 66

Step-by-step explanation:

Mean test scores = u = 74.2

Standard Deviation = = 9.6

According to the given data, following is the range of grades:

Grade A: 85% to 100%

Grade B: 55% to 85%

Grade C: 19% to 55%

Grade D: 6% to 19%

Grade F: 0% to 6%

So, the grade D will be given to the students from 6% to 19% scores. We can convert these percentages to numerical limits using the z scores. First we need to to identify the corresponding z scores of these limits.

6% to 19% in decimal form would be 0.06 to 0.19. Corresponding z score for  0.06 is -1.56 and that for 0.19 is -0.88 (From the z table)

The formula for z score is:

For z = -1.56, we get:

For z = -0.88, we get:

Therefore, a numerical limits for a D grade would be from 59 to 66 (rounded to nearest whole numbers)

30 people weigh 160 pounds or more

to determine the unit cost your would divide the total cost by the number sold.

7 bagels for $4.41       $4.41/7 = $.63 each at fresh side

5 bagels for $3.60         $3.60/5 = $.72 each at value mart