Question

) Final averages are typically normally distributed with a mean of 72 and a standard deviation of 12.5. Your professor states that the top 8% of the class will receive an A; the next 20% will receive a B; the next 42% will receive a C; the next 18% will receive a D; and the bottom 12% will receive an F. What grade must you exceed in order to receive a grade of C or better

Answer 1

65.45

Explanation:

Zscore = (x - mean) / standard deviation

x = score

Percentage below C :

D = 18% ; F = 12%

Sum = 30%

Obtain the Zscore for the proportion below D

P(Z < 0.30) = -0.524

Hence, Zscore = -0.524

Put Zscore = -0.524 in the equation :

-0.524 = (x - 72) / 12.5

-0.524 * 12.5 = x - 72

-6.55 = x - 72

-6.55 + 72 = x

x = 65.45

To receive a grade of C or better, score must be atleast 65.45