Question

What is the answer here?

The Principal decided that the top 30% of the class with the highest grades in statistics will be awarded. The scores are rounded off to the nearest hundredths and are approximately normally distributed with a mean of 80.51 and a standard deviation of 10.2.

7. What is the minimum score that a student should have to be awarded? Show your solution and shade the region under the curve that represents the portion of the population involved in the situation. (5 points)

Answer 1

Answer:

The minimum score that a student should have to be awarded is 85.916

Step-by-step explanation:

• Normal distribution is the stastical distribution in which the data is distributed around the mean.
• The distribution is converted to standard normal distibution by finding value of z and then determining the probability of z from the standard normal table.

       $Z=\frac{x-mean}{Standard\ deviation}$

Step 1 of 1:

• The top 30% students will get the award. Then the z value will be taken for the 50-30 i.e. 20% probability from mean.
• The value of z from the table is 0.53
• Mean of the distribution is 80.51
• Standard deviation of the distribution is 10.2
• The value of the minimum marks is given by x

       $Z=\frac{x-mean}{Standard\ deviation}$

       $0.53=\frac{x-80.51}{10.2} \\x=85.916$