\(\displaystyleμ={9.12}\)

ᵟ=Standard deviation=0.05

The z-score the value decreased by the mean, divided by the standard deviation.

\(\displaystyle{z}={\left(\frac{{{x}-μ}}{

Question

asked 2020-10-21

Assume that when adults with smartphones are randomly selected, 54% use them in meetings or classes (based on data from an LG Smartphone survey). If 8 adult smartphone users are randomly selected, find the probability that exactly 6 of them use their smartphones in meetings or classes.

asked 2021-05-05

The bulk density of soil is defined as the mass of dry solidsper unit bulk volume. A high bulk density implies a compact soilwith few pores. Bulk density is an important factor in influencing root development, seedling emergence, and aeration. Let X denotethe bulk density of Pima clay loam. Studies show that X is normally distributed with \(\displaystyle\mu={1.5}\) and \(\displaystyle\sigma={0.2}\frac{{g}}{{c}}{m}^{{3}}\).

(a) What is thedensity for X? Sketch a graph of the density function. Indicate onthis graph the probability that X lies between 1.1 and 1.9. Findthis probability.

(b) Find the probability that arandomly selected sample of Pima clay loam will have bulk densityless than \(\displaystyle{0.9}\frac{{g}}{{c}}{m}^{{3}}\).

(c) Would you be surprised if a randomly selected sample of this type of soil has a bulkdensity in excess of \(\displaystyle{2.0}\frac{{g}}{{c}}{m}^{{3}}\)? Explain, based on theprobability of this occurring.

(d) What point has the property that only 10% of the soil samples have bulk density this high orhigher?

(e) What is the moment generating function for X?

(a) What is thedensity for X? Sketch a graph of the density function. Indicate onthis graph the probability that X lies between 1.1 and 1.9. Findthis probability.

(b) Find the probability that arandomly selected sample of Pima clay loam will have bulk densityless than \(\displaystyle{0.9}\frac{{g}}{{c}}{m}^{{3}}\).

(c) Would you be surprised if a randomly selected sample of this type of soil has a bulkdensity in excess of \(\displaystyle{2.0}\frac{{g}}{{c}}{m}^{{3}}\)? Explain, based on theprobability of this occurring.

(d) What point has the property that only 10% of the soil samples have bulk density this high orhigher?

(e) What is the moment generating function for X?

asked 2021-05-27

The following table represents the Frequency Distribution and Cumulative Distributions for this data set: 12, 13, 17, 18, 18, 24, 26, 27, 27, 30, 30, 35, 37, 41, 42, 43, 44, 46, 53, 58
Class Frequency Relative Cumulative
Frequency Frequency
10 but less than 20 5
20 but less than 30 4
30 but less than 4 4
40 but less than 50 5
50 but less than 60 2
TOTAL
What is the Relative Frequency for the class: 50 but less than 60?
State you answer as a value with exactly two digits after the decimal. for example 0.30 or 0.35

asked 2021-06-09

The following table represents the Frequency Distribution and Cumulative Distributions for this data set: 12, 13, 17, 18, 18, 24, 26, 27, 27, 30, 30, 35, 37, 41, 42, 43, 44, 46, 53, 58
Class Frequency Relative Cumulative
Frequency Frequency
10 but less than 20 5
20 but less than 30 4
30 but less than 4 4
40 but less than 50 5
50 but less than 60 2
TOTAL
What is the Relative Frequency for the class: 20 but less than 30?
State you answer as a value with exactly two digits after the decimal. for example 0.30 or 0.35

asked 2021-05-11

The following table represents the Frequency Distribution and Cumulative Distributions for this data set: 12, 13, 17, 18, 18, 24, 26, 27, 27, 30, 30, 35, 37, 41, 42, 43, 44, 46, 53, 58
Class Frequency Relative Cumulative
Frequency Frequency
10 but less than 20 5
20 but less than 30 4
30 but less than 4 4
40 but less than 50 5
50 but less than 60 2
TOTAL
What is the Relative Frequency for the class: 40 but less than 50?
State you answer as a value with exactly two digits after the decimal. for example 0.30 or 0.35

asked 2021-05-05

A random sample of \( n_1 = 14 \) winter days in Denver gave a sample mean pollution index \( x_1 = 43 \).

Previous studies show that \( \sigma_1 = 19 \).

For Englewood (a suburb of Denver), a random sample of \( n_2 = 12 \) winter days gave a sample mean pollution index of \( x_2 = 37 \).

Previous studies show that \( \sigma_2 = 13 \).

Assume the pollution index is normally distributed in both Englewood and Denver.

(a) State the null and alternate hypotheses.

\( H_0:\mu_1=\mu_2.\mu_1>\mu_2 \)

\( H_0:\mu_1<\mu_2.\mu_1=\mu_2 \)

\( H_0:\mu_1=\mu_2.\mu_1<\mu_2 \)

\( H_0:\mu_1=\mu_2.\mu_1\neq\mu_2 \)

(b) What sampling distribution will you use? What assumptions are you making? NKS The Student's t. We assume that both population distributions are approximately normal with known standard deviations.

The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.

The standard normal. We assume that both population distributions are approximately normal with known standard deviations.

The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations.

(c) What is the value of the sample test statistic? Compute the corresponding z or t value as appropriate.

(Test the difference \( \mu_1 - \mu_2 \). Round your answer to two decimal places.) NKS (d) Find (or estimate) the P-value. (Round your answer to four decimal places.)

(e) Based on your answers in parts (i)−(iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level \alpha?

At the \( \alpha = 0.01 \) level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

At the \( \alpha = 0.01 \) level, we reject the null hypothesis and conclude the data are statistically significant.

At the \( \alpha = 0.01 \) level, we fail to reject the null hypothesis and conclude the data are statistically significant.

At the \( \alpha = 0.01 \) level, we reject the null hypothesis and conclude the data are not statistically significant.

(f) Interpret your conclusion in the context of the application.

Reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution index for Englewood and Denver.

Reject the null hypothesis, there is sufficient evidence that there is a difference in mean pollution index for Englewood and Denver.

Fail to reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution index for Englewood and Denver.

Fail to reject the null hypothesis, there is sufficient evidence that there is a difference in mean pollution index for Englewood and Denver. (g) Find a 99% confidence interval for

\( \mu_1 - \mu_2 \).

(Round your answers to two decimal places.)

lower limit

upper limit

(h) Explain the meaning of the confidence interval in the context of the problem.

Because the interval contains only positive numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is greater than that of Denver.

Because the interval contains both positive and negative numbers, this indicates that at the 99% confidence level, we can not say that the mean population pollution index for Englewood is different than that of Denver.

Because the interval contains both positive and negative numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is greater than that of Denver.

Because the interval contains only negative numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is less than that of Denver.

asked 2021-01-19

Find the probability that a randomly selected value is between 71.4 and 78.

\(\displaystyle{P}{\left({71.4}{<}{x}{<}{78}\right)}={P}{\left({<}{z}{<}\right)}=\)?

asked 2021-02-21

Subjects for the next presidential election poll are contacted using telephone numbers in which the last four digits are randomly selected (with replacement). Find the probability that for one such phone number, the last four digits include at least one 0.

asked 2021-03-05

1950 randomly selected adults were asked if they think they are financially better off than their parents. The following table gives
the two-way classification of the responses based on the education levels of the persons included in the survey and whether they
are financially better off, the same as, or worse off than their parents

\(\begin{array}{|c|c|c|}\hline &\text{Less Than High School}&\text{High School}&\text{More Than High School}\\\hline \text{Better off} &140&440&430\\ \hline \text{Same as}&60&230&110\\ \hline \text{Worse off}&180&280&80\\ \hline\end{array}\\\)

Suppose one adult is selected at random from these 1950 adults. Find the following probablity.

Round your answer to three decimal places.

\(P(\text{more than high school or worse off})=?\)

\(\begin{array}{|c|c|c|}\hline &\text{Less Than High School}&\text{High School}&\text{More Than High School}\\\hline \text{Better off} &140&440&430\\ \hline \text{Same as}&60&230&110\\ \hline \text{Worse off}&180&280&80\\ \hline\end{array}\\\)

Suppose one adult is selected at random from these 1950 adults. Find the following probablity.

Round your answer to three decimal places.

\(P(\text{more than high school or worse off})=?\)

asked 2021-01-25

A survey of 4826 randomly selected young adults (aged 19 to 25 ) asked, "What do you think are the chances you will have much more than a middle-class income at age 30?" The two-way table summarizes the responses. \(\begin{array} {lc} & \text{Gender} \ \text {Opinion} & \begin{array}{l|c|c|c} & Female & Male & Total \\ \hline \text{Almost no chance} & 96 & 98 & 194 \\ \hline \begin{array}{l} \text{Some chance but} \\ \text{probably not} \end{array} & 426 & 286 & 712 \\ \hline A\ 50-50\ chance & 696 & 720 & 1416 \\ \hline \text{A good chance} & 663 & 758 & 1421 \\ \hline \text{Almost certain} & 486 & 597 & 1083 \\ \hline Total & 2367 & 2459 & 4826 \end{array}\ \end{array}\)

Choose a survey respondent at random. Define events G: a good chance, M: male, and N: almost no chance. Find P(G | M). Interpret this value in context.