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This course is designed to acquaint the student with the principles of descriptive and inferential statistics. Topics will include: types of data, frequency distributions and histograms, measures of central tendency, measures of variation, probability, probability distributions including binomial, normal probability and student's t distributions, standard scores, confidence intervals, hypothesis testing, correlation, and linear regression analysis. This course is open to any student interested in general statistics and it will include applications pertaining to students majoring in athletic training, pre-nursing and business.

1

In a certain weather forecast comma the chances of a thunderstorm are stated as "1 in 16."

Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.

2

For a certain horse race, the odds in favor of a certain horse finishing in second place are given as 51 to 49.

Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.

3

Assume that 1200 births are randomly selected and exactly 607 of the births are girls.

Use subjective judgment to determine whether the given outcome is unlikely.

Determine whether it is unusual in the sense that the result is far from what is typically expected.

It is unlikely because the probability of this particular outcome is very small, considering all of the other possible outcomes.

*Recall that an event is unlikely if its probability is very
small, such as 0.05 or less. Consider the complement of the given
outcome and how likely it is.*

It is not unusual because 607 is about the number of girls expected.

4

Assume that 900 births are randomly selected and exactly 219 of the births are girls.

Use subjective judgment to determine whether the given outcome is unlikely.

Determine whether it is unusual in the sense that the result is far from what is typically expected.

5

You are
**certain** to get a black or a red card when
selecting cards from a shuffled deck.

Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.

6

It is
**impossible** to get 8 aces when selecting cards
from a shuffled deck.

Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.

7

You toss a coin and randomly select a number from 0 to 9.

What is the probability of getting tails and selecting a 5?

8

A random number generator is used to select a number from 1 to 100. What is the probability of selecting the number 149?

9

10

Among respondents asked which is their favorite seat on a plane, 487 chose the window seat, 10 chose the middle seat, and 310 chose the aisle seat.

What is the probability that a passenger prefers the middle seat?

Is it unlikely for a passenger to prefer the middle seat?

If so, why is the middle seat so unpopular?

The probability that a passenger prefers the middle seat is 0.012.

Yes, because the probability that a passenger prefers the middle seat is less than 0.05.

The middle seat lacks an outside view, easy access to the aisle, and a passenger in the middle seat has passengers on both sides instead of on one side only.

11

In a certain weather forecast, the chance of a thunderstorm is stated as 14%.

Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.

12

If A denotes some event, what does Ā denote?

If P(A) = 0.994, what is the value of P(Ā)?

If P(A) = 0.994, is Ā unusual?

13

In a genetic experiment on peas, one sample of offspring contained 385 green peas and 380 yellow peas.

Based on those results, estimate the probability of getting an offspring pea that is green.

Is the result reasonably close to the value of 3/4 that was expected?

14

Among 400 randomly selected drivers in the 16 – 18 age bracket, 269 were in a car crash in the last year.

If a driver in that age bracket is randomly selected, what is the approximate probability that he or she will be in a car crash during the next year?

It is unlikely for a driver in that age bracket to be involved in a car crash during a year?

Is the resulting value high enough to be of concern to those in the 16 – 18 age bracket? Consider an event to be "unlikely" if its probability is less than or equal to 0.05.

15

Among 450 randomly selected drivers in the 20 – 24 age bracket, 8 were in a car crash in the last year.

If a driver in that age bracket is randomly selected, what is the approximate probability that he or she will be in a car crash during the next year?

It is unlikely for a driver in that age bracket to be involved in a car crash during a year?

Is the resulting value high enough to be of concern to those in the 20 – 24 age bracket? Consider an event to be "unlikely" if its probability is less than or equal to 0.05.

16

A research center poll showed that 81% of people believe that it is morally wrong to not report all income on tax returns.

What is the probability that someone does not have this belief?

17

The following data lists the number of correct and wrong dosage amounts calculated by 33 physicians. In a research experiment, a group of 18 physicians was given bottles of epinephrine labeled with a concentration of "1 milligram in 1 milliliter solution," and another group of 15 physicians was given bottles labeled with a ratio of "1 milliliter of a 1:1000 solution."

If one of the physicians is randomly selected, find the probability of getting one who made a correct dosage calculation or was given the bottle with a concentration label.

18

What is wrong with the expression P(A) + P(**Ā**) = 0.5?

19

The probability that a randomly selected person refused to answer is
** 0.141**.

*P(refused)*

*= (total refused) ÷ (total people)*

*= 176 / 1249*

*= 0.1409127302*

** Yes, a high refusal rate results in a sample that is not
necessarily representative of the population, ** *b*
*ecause those who refuse may well constitute a particular group
with opinions different from others.*

20

In a computer instant messaging survey, respondents were asked to choose the most fun way to flirt, and it found that P(D) = 0.620, where D is directly in person.

If someone is randomly selected, what does P(D(–)) represent, and what is its value?

21

22

23

Pollsters are concerned about declining levels of cooperation among persons contacted in surveys. A pollster contacts 71 people in the 18-21 age bracket and finds that 66 of them respond and 5 refuse to respond. When 284 people in the 22-29 age bracket are contacted, 245 respond and 39 refuse to respond. Suppose that one of the 355 people is randomly selected.

Find the probability of getting someone in the 18 dash 21 age bracket or someone who refused to respond.

24

Determine whether the two events are disjoint for a single trial. (Hint: Consider "disjoint" to be equivalent to "separate" or "not overlapping".)

Randomly selecting a piano from the instrument assembly line and getting one that is free of defects.

Randomly selecting a piano from the instrument assembly line and getting one with a missing key.

25

Determine whether the two events are disjoint for a single trial. (Hint: Consider "disjoint" to be equivalent to "separate" or "not overlapping".)

Receiving a phone call from a volunteer survey subject who believes that there is solid evidence of global warming.

Receiving a phone call from a volunteer survey subject who is opposed to stem cell research.

26

What does P(B|A) represent?

27

A tire company produced a batch of 6,900 tires that includes exactly 250 that are defective.

**a.** If 4 tires are randomly selected for installation
on a car, what is the probability that they are all good?

**b.** If 100 tires are randomly selected for shipment to
an outlet, what is the probability that they are all good?

**c. **Should this outlet plan to deal with defective
tires returned by consumers?

28

For the given pair of events A and B, complete parts (a) and (b) below.

A: When a baby is born, it is a boy.

B: When a 5-sided die is rolled, the outcome is 4.

**a.** Determine whether events A and B are independent
or dependent. (If two events are technically dependent but can be
treated as if they are independent according to the 5% guideline,
consider them to be independent.)

**b.** Find P(A and B), the probability that events A
and B both occur.

29

For the given pair of events A and B, complete parts (a) and (b) below.

A: A marble is randomly selected from a bag containing 11 marbles consisting of 1 red, 4 blue, and 6 green marbles. The selected marble is one of the green marbles.

B: A second marble is selected and it is the 1 red marble in the bag.

**a.** Determine whether events A and B are independent
or dependent. (If two events are technically dependent but can be
treated as if they are independent according to the 5% guideline,
consider them to be independent.)

**b.** Find P(A and B), the probability that events A
and B both occur.

30

Describe what the notation P(B|A)represents.

31

The principle of redundancy is used when system reliability is improved through redundant or backup components. Assume that a student's alarm clock has a 8.4% daily failure rate.

**a. **What is the probability that the student's alarm
clock will not work on the morning of an important final exam?

**b.** If the student has two such alarm clocks, what is
the probability that they both fail on the morning of an important
final exam?

**c.** What is the probability of not being awakened if
the student uses three independent alarm clocks?

**d.** Do the second and third alarm clocks result in
greatly improved reliability?

33

Assume that a company hires employees on Mondays, Tuesdays, or Wednesdays with equal likelihood.

**a.** If two different employees are randomly selected,
what is the probability that they were both hired on a Monday?

**b.** If two different employees are randomly selected,
what is the probability that they were both hired on the same day of
the week?

**c.** What is the probability that 7 people in the same
department were all hired on the same day of the week?

**d.** Is such an event unlikely?

34

35

The accompanying table contains the results from experiments with a polygraph instrument.

**a.** Four of the test subjects are randomly selected
with replacement, and they all had true negative test results. Is
such an event unlikely?

**b.** Four of the test subjects are randomly selected
without replacement, and they all had true negative test results. Is
such an event unlikely?

**a.** The probability that all four test subjects had a
true negative test result when they are randomly selected with
replacement is **0.083**.

**No, because the probability of the event is greater than 0.05.**

*(66/123) ^{4} = 0.0829001462*

**b. **The probability that all four test subjects had a
true negative test result when they are randomly selected without
replacement is **0.079**.

**No, because the probability of the event is greater than 0.05.**

*(66/123) x (65/122) x (64/121) x (63/120) = 0.0793864272*

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