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A teacher 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 ?

Respuesta :

Answer:

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

[tex]z=[tex]\frac{x-74}{6}[/tex][/tex] 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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