Workshop 4 The Normal Distribution
Date Completed: _____________ |

Provide all solutions, answers and requested outputs after each question.

**Question 1**: The normal distribution of IQ scores is 100 with
a standard deviation of 15.

If an individual with a tested IQ
of 70 or below is considered mentally retarded,

what percentage of the population
would be classified retarded?

**Question 2**: If the range of "average" IQ scores is 90 to 110,
what percentage of the population is

considered average in
intelligence?** **

**Question 3. ** Assume a random sample, *X* is taken from
the following distribution, compute

their z-scores and use the
standard normal distribution table to compute their

cumulative probabilities.

*
X = {12, 14, 23, 13, 15, 20, 14,
18, 17, 15}*

**Question 4. **For a population with mean of m = 70, a score of
62 corresponds to a z-score of z = -2.00.

What is the population standard
deviation? (hint, use the z-score formula and

solve for the unknown or *SD*)

**Question** **5**. Bill earned a score of X = 73 on an
English test with a mu = 65 and the s = 8. John, his best friend,

earned a score of X = 63 on a
math test with a m = 57 and s = 3. Who should the better grade?

Explain your answer. (Hint: use
the concept of percentile rank)

**Question 6. **Use a statistical software the compute the *z*-scores
for all the scores of an experiment for weight gain, *
X* in pounds, of the following
12 females:

Subjects | Mary | Ann | Sue | Lisa | Kim | Jen | Wendy | Rose | Toni | Frans | Beth | June |

Weight Changes |
11.4 |
11 |
5.5 |
9.4 |
13.6 |
-2.9 | -0.1 |
7.4 |
21.5 |
-5.3 | -3.8 |
13.4 |

**Question 7. **A number of years ago the mean and the standard
deviation on the Graduate Record Exam

(GRE) for all people taking the
exam were 489 and 126 respectively.

What percentage of students would
be expected to have a score for 600 of less?

(This is called the percentile
rank of 600)

**Question 8. ** Scores on the SAT standardized exam has a
normal distribution with mean = 500 and *SD* = 100.

What is the minimum score needed
to be in the top 20% on the SAT exam?

(Hint, find the 80 percentile for
the SAT).

**Question 9. ** To find the 95% Confidence Interval (the
interval, symmetrical about the mean where 95% of the

distribution lies) for a sample
distribution with mean, *M* = 50 and standard deviation, *SD*
= 10,

we must find the 2.5 percentile
and then the 97.5 percentile. What is the 95%

**Question 10**: (a) Use a statistical package and compute
the *z*-score for the pass4th variable of the ODE.csv dataset.

(b) How many
scores are greater than *z* = +2? Paste your output here.