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Suppose that, for a certain mathematics class, the scores are normally distributed with a mean of 75 and a standard deviation of 6. The teacher wishes to give A's to the top 5% of the students and F's to the bottom 5%. The next 15% in either direction will be given B's and D's, with the other students receiving C's. Find the bottom cutoff for receiving an A grade. (You may need to use the standard normal distribution table. Round your answer to the nearest whole number.)

Respuesta :

Answer:

84.87

Step-by-step explanation:

Let X be the Math score of the mathematics class referred

Then given that X is N(75,6)

Or [tex]z=\frac{x-75}{6}[/tex] is N(0,1)

For z score top 5% cut off score is from 1.645

Corresponding X score can be calculated from this

[tex]x=\mu+\sigma*z\\X = 75+6(1.645) = 75+9.870\\X=84.870[/tex]

Whoever got about 84.87 will be given A grade.

the bottom cutoff for receiving an A grade.

=84.87