Ateacher gives a test to a large group of students. the results are closely approximated by a normal curve. the mean is 74 with a standard deviation of 6. the teacher wishes to give a's to the top 8% of the students and f's to the bottom 8%. a grade of b is given to the next 15%, with d's given similarly. all other students get c's. find the bottom cutoff (rounded to the nearest whole number) for a b. (hint: use a table of areas under the standard normal curve to find z-scores from known a-values.) the bottom cutoff for a b is ?

82.46

Step-by-step explanation:

Given that the results of a test to a large group given by a teacher (X)

is normal with mean = 74 and std dev =6

X: N(74,6)

Hence

" alt="\frac{x-74}{6}" />" /> is N(0,1)

WE have to find out the bottom cut off for grade B.

B is between 8 and 23%

From std normal distribution we find Z values such that

P(Z>c1) = 0.08 and P(Z>c2) =0.23

c1=1.41: c2=0.74

Corresponding x values are

74+6(1.41) and 84+6(0.74)

i.e. 82.46 and 88.74

Thus bottom cut off for a B is 82.46

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step-by-step explanation: