A recent poll by the American Automobile Club found that 74.5% of those surveyed are worried about aggressive drivers on the road. If three people are selected at random, what is the probability that (Show how you get these either by formula or calculator)4.) none will be worried about aggressive drivers on the road?5.) one will be worried about aggressive drivers on the road?6.) all will be worried about aggressive drivers on the road?7.) two will be worried about aggressive drivers on the road?8.) at least one will be worried about aggressive drivers on the road? 9.) at most two will be worried about aggressive drivers on the road?

Question
Asked Jun 10, 2019
63 views

A recent poll by the American Automobile Club found that 74.5% of those surveyed are worried about aggressive drivers on the road. If three people are selected at random, what is the probability that (Show how you get these either by formula or calculator)

4.) none will be worried about aggressive drivers on the road?
5.) one will be worried about aggressive drivers on the road?
6.) all will be worried about aggressive drivers on the road?
7.) two will be worried about aggressive drivers on the road?
8.) at least one will be worried about aggressive drivers on the road? 9.) at most two will be worried about aggressive drivers on the road?

check_circle

Expert Answer

Step 1

Hey there! Thank you for posting the question. As your question has more than 3 parts, we have solved the first 3 parts for you. If you need help with any other particular part, please re-post the question and mention the part you need to be answered.

Step 2

In this context, a random experiment involving n independent trials, such that the outcome of each trial can be classified as either a “success” or a “failure”. The numerical value “1” is assigned to each success and “0” is assigned to each failure.

Moreover, the probability of getting a success in each trial, p, remains a constant for all the n trials. Denote the probability of failure as q. As success and failure are mutually exclusive, q = 1 – p.

Let the random variable X denote the number of successes obtained from the n trials. Thus, X can take any of the values 0,1,2,…,3.

Then, the probability distribution of X is a Binomial distribution with parameters (n, p) and the probability mass function (pmf) of X, that is, of a Binomial random variable, is given as:

help_outline

Image Transcriptionclose

пn |P'a*. х 3D0,1....n;:0 <p<1;g31-р Р(к) otherwise [0,

fullscreen
Step 3

Parameters of binomial distribution for the given situation:

The size of the sample taken from the population of people is n = 3. It is known that people who is worried and not worried, implying independence among each other. As a result, 3 respondents may be considered as 3 independent trials.

Consider the event that the people who is worried about the aggressive drivers as a “success”. It is given that 74.5% of respondents were worried about aggressive drivers. Thus, the probability that the people who is worried about the aggressive drivers, that...

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Statistics

Hypothesis Testing

Related Statistics Q&A

Find answers to questions asked by student like you
Show more Q&A
add
question_answer

Q: 10 9 8 6 Frequency 5 4 3 2 1 0 to 9 10 to 19 20 to 29 30 to 39 40 to 49 50 to 59 The table above lis...

A: Frequency table:Frequency table represents the number of times each class repeats.The frequency of e...

question_answer

Q: a. Using the pairs of values for all 10​points, find the equation of the regression line. b. After r...

A: Part (a):From the graph, the data points are (1,7),(1,8),(1,9),(2,7),(2,8),(2,9),(3,7),(3,8),(3,9),a...

question_answer

Q: Directions: Draw the normal curve and shade the specific region show formulas     A random same of 2...

A: Confidence interval:The (1-α) % confidence interval for proportion p is given by,

question_answer

Q: A store sells bags of candy that weigh exactly 2lb, according to their packaging. Elena, the store m...

A: It is given that the store sells bags of weight, exactly 2lb. The claim is that the population mean ...

question_answer

Q: Please answer the whole question.  (1) Let x be the age in years of a licensed automobile driver. Le...

A: (e) The value of coefficient of determination:The given data is represented in the following table:

question_answer

Q: Jane has stored three albums on her iPod. The first album consists of 11 songs by Frank Sinatra, the...

A: According to the given question, Jane has stored three albums on her iPod.The first album consists o...

question_answer

Q: Statistics Question

A: Solution:It is given that “Budget” as x variable and significance level of α=0.05.The regression equ...

question_answer

Q: Are there ever any circumstances when a correlation such as Pearson's r can be interpreted as eviden...

A: Correlation between any two variables tell us the linear association meaning that one variable rise ...

question_answer

Q: 1. In a random sample of 15 CD players brought in form repair, the average repair cost was $80 and t...

A: It is given that the average repair cost (mean) is $80, sample standard deviation s is $14, the samp...