Download Name: Period: Date: Introduction to Statistics – Normal Distribution

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Period:
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Introduction to Statistics – Normal Distribution and Z-Scores
Suppose 𝜇 = 25 and 𝜎 = 5.5.
Label the normal model to help you answer the following
THREE questions:
7. We are interested in estimating the number of students
at a large high school who are going to attend the school
dance this weekend. We ask 40 random students if they
are planning on attending. Are the 40 students surveyed
considered a sample or a population? Explain.
8. Suppose 2.3 is the true mean of a population. Explain
why -1.1 is not a possible z-score for an actual score of 3.5?
9. Find 𝜇, given 𝜎 = 2 , if an actual score of 3.8 has a z𝑥−𝜇
score of 3. Use the formula 𝑧 =
.
𝜎
1. What score is 3 standard deviations above the mean?
2. What percent of the population falls between 14 and 36?
10. Find the area of the shaded region. The graph depicts
the standard normal distribution with mean 0 and
standard deviation 1.
3. What is the probability a randomly selected person falls
between 19.5 and 30.5?
4. The mean age of a study group for a statistics class at a
local community college was 26. The standard deviation was
3 years. If you are 22 years old, what is your z-score?
Interpret the z-score in words.
5. The mean GPA of a local high school is 2.9. The GPA’s are
approximately normally distributed with a standard
deviation of 0.4. If John has a GPA if 3.3, at what approximate
what percent of the school has a GPA lower than John?
–3
–2
–1
0
1
2
3
11. Find the area of the shaded region. The graph depicts
the standard normal distribution with mean 0 and
standard deviation 1.
–3
–2
–1
0
1
2
3
12. Find the area of the shaded region. The graph depicts
the standard normal distribution with mean 0 and
standard deviation 1.
6. Using the 68-95-99.7 rule, approximately what percent of
a normally distributed population falls between -2 and 0
standard deviations from the mean?
2
0
13. Find the area of the shaded region. The graph depicts the
standard normal distribution with mean 0 and standard
deviation 1.
–2
–1
16. A Spanish club is electing a president, vice president,
and secretary. The club has nine members who are eligible
for these offices. How many different ways can the offices
be filled?
0
14. Find the area of the shaded region. The graph depicts the
standard normal distribution with mean 0 and standard
deviation 1.
17. Poker hand is a card game that 5 cards are randomly
select from a deck of 52 playing card. What is the
probability of getting two pairs and one other card?
(Example: Ace Ace, King King , Queen)
–1
0
15. Find the area of the shaded region. The graph depicts the
standard normal distribution with mean 0 and standard
deviation 1.
–1
18. From a pool of potential jurors of 14 women and 13
men? What is the probability of selecting 12 jurors that
must have at least 10 men?
2
0
Use the following graph created from a simulation to answer the next 3 questions: The graph shows a simulation with 50 fill up trials.
19. What is the probability of achieving
between 285 and 299 miles?
20. According the graph representing the number of
miles a car can drive on a single tank (from a simulation
of 50 tank fillups), what is the probability of achieving
LESS THAN 275 miles?
21. Which of the following is the least likely to occur?
a.
Achieving greater than or equal to 290 miles per tank.
b.
Achieving less than 269 miles per tank.
c.
Achieving between 285-289 miles per tank.
d.
Achieving between 280-289 miles per tank.