SAT College

Assume that when adults with smartphones are randomly selected, 49% use them in meetings or classes. If 15 adult smartphone users are randomly selected find the probability that fewer than 3 of them use their smartphones in meetings or classes.

Answers

Answer 1
We can calculate the probability of having less than 3 smartphone users among 15 users by using the binomial distribution formula, which is given by:

P(k;n,p) = C(n,k) * p^k * (1-p)^(n-k)

Where:

k is the number of successful outcomes, in this case the number of smartphone users who use their devices in meetings or classes
n is the total number of trials, in this case the total number of smartphone users we are selecting
p is the probability of success, in this case the probability that a smartphone user uses their device in meetings or classes
First, we need to calculate the probability that exactly 0 smartphone users use their devices in meetings or classes. This is given by:

P(0;15,0.49) = C(15,0) * 0.49^0 * (1-0.49)^15 = 0.26

Next, we need to calculate the probability that exactly 1 smartphone user uses their device in meetings or classes. This is given by:

P(1;15,0.49) = C(15,1) * 0.49^1 * (1-0.49)^14 = 0.33

Finally, we need to calculate the probability that exactly 2 smartphone users use their devices in meetings or classes. This is given by:

P(2;15,0.49) = C(15,2) * 0.49^2 * (1-0.49)^13 = 0.15

The probability of having fewer than 3 smartphone users among 15 users is given by the sum of the probabilities of having 0, 1, or 2 smartphone users, which is 0.26 + 0.33 + 0.15 = 0.74. This means that there is a 74% probability that fewer than 3 of the 15 selected smartphone users use their devices in meetings or classes.
Answer 2

The probability that fewer than 3 of the 15 smartphone users use their phones in meetings or classes is 7.46%.

What is the binomial probability theorem?

The binomial probability formula.

P(X = k) = [tex]^nC_r[/tex] [tex]P^k[/tex] [tex](1 - P)^{n - k}[/tex]

where n is the sample size, k is the number of successes, P is the probability of success, (P - 1) is the failure.

We have,

The required probability.

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

Where X is the number of smartphone users out of 15 who use their phones in meetings or classes.

Now,

Using the binomial probability.

P(X = k) = [tex]^nC_r[/tex] [tex]P^k[/tex] [tex](1 - P)^{n - k}[/tex]

where n is the sample size, k is the number of successes (using their smartphones in meetings or classes), p is the probability of success (49%), and (n choose k) is the number of ways to choose k successes out of n trials.

We get,

P(X = 0) = [tex]^{15}C_0[/tex] x [tex]0.49^0[/tex] x [tex]0.51^{15}[/tex] = 0.0018

P(X = 1) = [tex]^{15}C_1[/tex] x [tex]0.49^1[/tex] x [tex]0.15^{14}[/tex] = 0.0149

P(X = 2) = [tex]^{15}C_2 \times 0.49^2 \times 0.49^{13}[/tex] = 0.0579

The probability of fewer than 3 smartphone users using their phones in meetings or classes.

P(X < 3)

= P(X = 0) + P(X = 1) + P(X = 2)

= 0.0018 + 0.0149 + 0.0579

= 0.0746

= 0.0746 x 100

= 7.46%

Thus,

The probability that fewer than 3 of the 15 smartphone users use their phones in meetings or classes is 7.46%.

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Related Questions

When communicating with parents for a meeting which is the most effective way to do it

Answers

Note that when communicating with parents for a meeting, the most effective way to do it is to make it an in-person communication.

What is in-person communication and why is it important?

In-person communication is precisely what it sounds like, and it is one of the most successful methods of forming parent connections. In-person communication is used whenever you interact with a parent in person.

Communication in our daily lives helps us develop connections by allowing us to share our experiences and needs, as well as connect with others. It is the vitality of life, allowing us to express our emotions, convey information, and share our opinions. We must all communicate.

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Number of College Faculty The number of
faculty listed for a variety of private colleges that offer
only bachelor’s degrees is listed below. Use these data
to construct a frequency distribution with 7 classes, a
histogram, a frequency polygon, and an ogive. Discuss
the shape of this distribution. What proportion of
schools have 180 or more faculty?
165 221 218 206 138 135 224 204
70 210 207 154 155 82 120 116
176 162 225 214 93 389 77 135
221 161 128 310

Answers

A frequency polygon displays class frequencies while an ogive displays cumulative frequencies.

Is an ogive and a frequency polygon the same?A frequency polygon is a line graph while an orgive is a histogram . A frequency polygon displays class frequencies while an orgive displays cumulative frequencies there is no difference between a frequency polygon and ogive.The area under the frequency polygon is the same as the area under the histogram and is, therefore, equal to the frequency values that would be displayed in a distribution table. The frequency polygon also shows the shape of the distribution of the data, and in this case, it resembles a bell curve.The frequency polygon is a curve that is drawn on the x-axis and the y-axis. The x-axis represents the values in the dataset, while the y-axis shows the number of occurrences of each distinct category.An Ogive Chart is a curve of the cumulative frequency distribution or cumulative relative frequency distribution. For drawing such a curve, the frequencies must be expressed as a percentage of the total frequency.

Procedure to find 5 number summary -

Step 1: First we need to arrange the date set in ascending order.

Step 2: Find minimum and maximum number in the data set.

Step 3: Find Median.

Median = Median is the center element (Ascending order)

Step 4: Find Q1 and Q2

Q1 is the median in the lower half of the data, and Q3 is the median in the upper half of data.

Now, consider the given numbers -

224, 203, 207, 201, 212, 225, 196, 221, 210, 195, 206, 206, 221, 191, 217

Here,

Ascending order : 191, 195, 196, 201, 203, 206, 206, 207, 210, 212, 217, 221, 221, 224, 225

Minimum : 191

Maximum : 225

First Quartile(Q1) : 201

Third Quartile(Q2) : 221

Median : 207

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how to develop an e portfolio
​

Answers

Answer:

1. Decide on the purpose of your e portfolio. Ask yourself why you are creating the e portfolio. Consider what you want to communicate and the audience you are targeting.

2. Gather the content you want to include in your e portfolio. This could include resumes, work samples, awards, certifications, and other relevant documents.

3. Choose a platform for your e portfolio. There are many online tools that can help you create an e portfolio, such as WordPress, Weebly, Wix, and Squarespace.

4. Design your e portfolio. Consider the overall look and feel that you want to achieve. Think about the colors, fonts, and images you want to use.

5. Upload your content to your e portfolio. Make sure to include descriptions and captions for each item.

6. Test your e portfolio. Check for any errors or typos and make sure that all links are working properly.

7. Publish your e portfolio. Once you are satisfied with the final product, you can share it with your intended audience.

Explanation:

Classify the following data. Indicate whether the data is qualitative or quantitative, indicate whether the data is discrete, continuous, or neither, and indicate the level of measurement for the data.

Survey responses to the question "In which of the following regions of the country do you live?"

1) East 2) North 3) South 4) West

Answers

Survey responses to the question. The regions are:

1) East: Qualitative.

2) North: Neither.

3) South: Nominal.

4) West: continuous.

What is nominal data?

Variables with no numerical value are labeled using nominal data. Male/female (albeit slightly archaic), hair color, ethnicities, names of people, etc. are typical instances.

Data is information that has been transformed into a format that is useful for transfer or processing in computing. Data is information that has been transformed into binary digital form for use with modern computers and communication mediums.

Therefore, the correct option is 1) East: Qualitative. 2) North: Neither. 3) South: Nominal, and 4) West: continuous.

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