Question about basic statistics

Question

anonymous · Answer

Percentage grades in a large biology class follow a normal distribution with standard deviation 6.3.  It is known that 20% of students receive grades higher than 74.29.  What is the mean grade in the class?

anonymous · Answer

can you help me?

kropot72 · Answer

The percentage of students receiving less than 74.29 = 100 - 20 = 80%.
Reference to a standard normal distribution table shows that the z-score corresponding to 0.8 cumulative probability is 0.842.
To find the mean grade in the class we can use the following equation:
$$z=\frac{X-\mu}{\sigma}\ .........(1)$$
Substituting the known values into equation (1) gives:
$$0.842=\frac{74.29-\mu}{6.3}$$
You need to solve this equation to find the value of mu the mean grade.

anonymous · Answer

68.9854

kropot72 · Answer

Good work. That is the correct value of the mean grade :)