Download MA116 Guided activity 6 2

MA117 Guided Activity 6.2 – due _______________
Probabilities for Bell Shaped Distributions – Read the book, and the examples on the section to answer
1. The Normal distributions are commonly used for what type of variable?
Discrete random variables
2.
or
continuous random variables
Give a bulleted summary of the characteristics of a normal distribution – read the box shown on page 277

3. The graphs shown on the top of page 277 correspond to what two distributions?
a) For each one give the individuals, variable with units
b) For each one give the mean mu and the standard deviation sigma
c) Why is the graph for men to the right of the graph for women?
d) Why is the graph for men lower than the graph for women?
e) Sketch the distributions of heights of adult women labeling along the axis the mean and one, two
and three standard deviations around the mean.
f)
Shade the area to the right of 72 inches
g) What is the z-score of 72?
h) What is the area to the left of 72? Use the table.
i)
What is the area to the right of 72? Show procedure.
j)
What is the probability of selecting at random a woman who is taller than 72 inches?
4. Sketch the distributions of heights of adult men labeling along the axis the mean and one, two and three
standard deviations around the mean. Shade the area between 65 and 70. Find the z score of each. Find the
area to the left of each. Calculate the area between 65 and 70.
5. What percent of men have heights between 65 and 70 inches tall?
6. Show all work that leads to the percentages used in the empirical rule
7. What is the standard normal distribution? Sketch and label. (pg. 285)
8. Finding probabilities with the calculator (we’ll do in class)
2nd VARS[DISTR], select 2:normalcdf(left, right, mean, standard deviation)
MA117 Guided activity 6.2 – (continued) - due _______________
Find scores in a normal distribution
Sketch, label mean, label and shade the given area to the left, read table from inside out to find the z-score, use the
formula to find the score x ( x    z )
1. Find the z-score for which the area under the standard normal curve to its left is 0.96. Sketch, shade.
2. Find the z-score for which the area under the standard normal curve to its left is 0.26. Sketch, shade.
3. Read example 7.
a) Give the variable?
b) Give the parameters with proper notation
c) Sketch, locate 98th percentile and label area to the left
d) Go to the table, read from inside out to determine the z-score
e) Use the formula x    z to find the score x
f)
The 98th percentile is
g)
h)
i)
j)
Draw another sketch, locate the 45th percentile and label the area to the left
Go to the table, read from inside out to determine the z-score
Use the formula to find x
The 45th percentile is
k) The IQ of Luis has an area to the right of 0.25. What is his percentile?
l) Find his IQ score
4. Finding scores with the calculator (we’ll do in class)
2nd VARS[DISTR], select 3:invNorm(area to the left, mean, standard deviation)