The following question has to do with statistics

Question

Maria Thomas a teacher at Henry elementray school noted grades of her students which were distributed with a mean of 74 and a standard deviation of 10. María thomas has informed us that 6.3 percent of his students received A's while only 2.5 percent of her st failed the course and received F's.

 

a) what is the minimum score needed to make an A?

 

 

b) what is the maximum score among those who received an F?

 

c) if there were 5 students who did not pass the course, how many students took the course?

Answer 1

Beatriz,

A true normal distribution has the mean = median = mode. While a lot of random data is close enough to that to call it "normal," perfectly conforming data is uncommon. The application works like this:

 

a)  6.3% is the accepted quantity of data points falling beyond 1.5 standard deviations above the mean. So:

      74 + 1.5(10) makes 89 the cutoff. 90 is the minimum A.

 

b)  2.5% is the typical quantity found beyond two standard deviations below the median. So:

      74 - 2(10) = 54 as the cutoff. 53 is the highest score receiving an F.

 

c)  5 = 2.5%T   ⇒   T = 5/.025 = 200 students took the course.