Normal Distribution

Standard scores and normal distribution 1

A normal score distribution has a mean of 60 and a standard deviation of 6. What percentage of scores lie: (a) below a score of 24? (b) below a score of 72? (c) above a score of 96?

2

A normal distribution has a mean of 45 and a standard deviation of 6. The number of scores in this distribution is 1200. What number of scores lie: (a) below 51? (b) above 57? (c) between 39 and 51?

3

A normal distribution has a mean of 38. What will be the median and the mode for this distribution?

4

If the scores of 500 students are normally distributed with a mean of 66.5 and a standard deviation of 2.8, how many students have scores: (a) greater than 70? (b) less than 60% (c) between 65 and 70? (d) between 60 and 65? 5

A normal distribution of scores has a mean of 62.5 and a standard deviation of 4. The number of students with a score greater tan 70.5 is 30. Calculate the number of students in this distribution.

6

A normal distribution of scores has a mean of 55. 47.32% of the students have a score between 55 and 61. What is the standard deviation of this distribution?

7

A grade 6 Mathematics teacher decided to assess the performance of 10 grade 6 learners pertaining to fractions. The learners then took part in a computer-based lesson on fractions for 1 hour per day for 2 weeks. Their performance where determined 3 weeks after the computer-based intervention. The raw scores of the two tests are given in the following table: Student Sam Joseph Bettie Maria John Ann Peter Linda George Martha

Score before 30 45 56 23 45 31 41 33 34 24

Score after 35 45 67 26 78 45 46 46 51 38

Calculate the percentage of learners that improved their performance.