Question

At Polk High School, 500 students took an algebra mastery test. The scores were distributed normally with a mean

of 75 and a standard deviation of 7.

Answer the following questions based on the data:

a) What percentage of scores are between scores 61 and 82?

b) What percentage of scores are between scores 75 and 82?

c) What percentage of scores are between scores 61 and 89?

d) What percentage of scores is less than a score of 61?

e) What percentage of scores is greater than a score of 96?

f)Approximately how many algebra students scored between 61 and 89? 764 students

g) Approximately how many algebra students scored between 68 and 82?

h) Approximately how many algebra students scored between 61 and 75?

i) Approximately how many algebra students scored between 89 and 96?

j) Approximately how many algebra students scored higher than 89?

Answer 1

a) 68% of scores are within 1 standard deviation of the mean, so 68% of scores are between 68 and 82.

b) 34% of scores are between the mean and 1 standard deviation above the mean, so 34% of scores are between 75 and 82.

c) 95% of scores are within 2 standard deviations of the mean, so 95% of scores are between 58 and 92.

d) 15.85% of scores are less than 1 standard deviation below the mean, so 15.85% of scores are less than 61.

e) 15.85% of scores are more than 1 standard deviation above the mean, so 15.85% of scores are greater than 96.

f) Approximately 475 students scored between 61 and 89, since 95% of students scored between 58 and 92.

g) Approximately 340 students scored between 68 and 82, since 68% of students scored between 68 and 82.

h) Approximately 235 students scored between 61 and 75, since 47.5% of students scored between 61 and 75.

i) Approximately 235 students scored between 89 and 96, since 47.5% of students scored between 89 and 96.

j) Approximately 250 students scored higher than 89, since 50% of students scored higher than the mean and 15.85% of students scored more than 1 standard deviation above the mean.

Answers:

a) 68%

b) 34%

c) 95%

d) 15.85%

e) 15.85%

f) 475 students

g) 340 students

h) 235 students

i) 235 students

j) 250 students