Question 1

Solve the problem.
-The numbers below represent the amount of precipitation, in inches, on January 1st in eleven different U.S. cities. Find the mean precipitation. Round your answer to the nearest ten-thousandth
Of an inch. $\begin{array} { l l l l l l } 0.152 & 0.072 & 0.146 & 0.099 & 0.079 & 0.108 \end{array}$
$\begin{array} { l l l l l } 0.151 & 0.087 & 0.109 & 0.131 & 0.082 \end{array}$
A) $0.108 \mathrm { in }$.
B) $0.1013 \mathrm { in }$.
C) $0.1105 \mathrm { in }$.
D) $0.1216 \mathrm { in }$.

Accepted Answer

The answer of Solve the problem.
-The numbers below represent the...

Question 2

State whether you would expect the data set to be normally distributed.
-Amount of credit card debt of families in the U.S.
A)Normal
B)Not normal

Accepted Answer

The amount of credit card debt of families in the U.S. is likely to be not normally distributed because it is expected to be right-skewed. Many families will have low to moderate debt, while a smaller number will have very high debt, leading to a long tail on the right side of the distribution.

Question 3

State whether you think the difference between what occurred and what you would expect by chance is statisticallysignificant.
-There are two candidates for mayor, Maria Hernandez, and Eric Wong. Of 100 people polled, 53 say they will vote for Maria Hernandez.
A)Not statistically significant
B)Statistically significant

Accepted Answer

Given the information provided, the difference between the observed outcome (53 out of 100 people favoring Maria Hernandez) and what would be expected by chance (50 out of 100, assuming no preference between the two candidates) is not large enough to be considered statistically significant without further statistical analysis, such as a p-value calculation.

Question 4

Construct a boxplot as requested.
-The test scores of 32 students are listed below. Construct a boxplot for the data set. $\begin{array} { l l l l l l l l } 32 & 37 & 41 & 44 & 46 & 48 & 53 & 55 \end{array}$
$\begin{array} { l l l l l l l l } 57 & 57 & 59 & 63 & 65 & 66 & 68 & 69 \end{array}$
$\begin{array} { l l l l l l l l } 70 & 71 & 74 & 74 & 75 & 77 & 78 & 79 \end{array}$
$\begin{array} { l l l l l l l l } 81 & 82 & 83 & 86 & 89 & 92 & 95 & 99 \end{array}$
A)

B)

C)

D)

Accepted Answer

The answer of Construct a boxplot as requested.
-The test scores...

Question 5

State whether you would expect the data set to be normally distributed.
-The diameters of the redwood trees in a forest.
A)Normal
B)Not normal

Accepted Answer

The diameters of redwood trees in a forest are likely to be normally distributed due to natural variation in growth, assuming the forest is mature and not recently disturbed.

Question 6

Obtain the five-number summary for the given data.
-The weights (in pounds)of 18 randomly selected adults are given below. $\begin{array} { l l l l l l } 120 & 145 & 187 & 153 & 119 & 138 \ 127 & 142 & 179 & 164 & 182 & 202 \ 114 & 174 & 130 & 149 & 167 & 174 \end{array}$
$\begin{array} { c c c c c } 114 & 174 & 130 & 149 & 167 \end{array}$
A)$114,128.50,149,170.5,202$
B) $114,130,151.0,174,202$
C) $114,129.25,151.0,175.25,202$
D) $114,128.50,151.0,170.5,202$

Accepted Answer

The answer of Obtain the five-number summary for the given...

Question 7

For the given data value, find the standard score and the percentile.
-A data value $1.3$ standard deviations above the mean.
A) $z = 1.3$; percentile $= 2.2$
B) $z = 0.13$; percentile $= 55.96$
C) $z = - 1.3$; percentile $= 9.68$
D) $z = 1.3$; percentile $= 90.32$

Accepted Answer

The standard score (z-score) is given as $1.3$, indicating the data value is $1.3$ standard deviations above the mean. The corresponding percentile for a $z$ score of $1.3$ is approximately $90.32$, indicating that about $90.32\%$ of the data falls below this value.

Question 8

State whether the distribution appears to be (roughly)normal.
-
A) Normal
B) Not normal

Accepted Answer

The answer of State whether the distribution appears to be...

Question 9

Use the 68-95-99.7 rule to solve the problem.
-At one college, GPA's are normally distributed with a mean of 3 and a standard deviation of 0.6. What percentage of students at the college have a GPA between 2.4 and 3.6?
A)99.7%
B)68%
C)95%
D)84%

Accepted Answer

The 68-95-99.7 rule states that approximately 68% of data falls within one standard deviation of the mean in a normal distribution. Here, 2.4 and 3.6 are one standard deviation below and above the mean (3 ± 0.6), so 68% of students have a GPA between 2.4 and 3.6.

Question 10

Find the margin of error for the survey results described.
-In a survey of 602 employees of a large company, 25% said that they had high job satisfaction. Give your answer as a decimal to three decimal places.
A)0.041
B)0.002
C)0.082
D)0.020

Accepted Answer

The margin of error for a proportion is calculated using the formula $ME = z \times \sqrt{\frac{p(1-p)}{n}}$, where $z$ is the z-score corresponding to the desired confidence level (typically 1.96 for 95% confidence), $p$ is the sample proportion, and $n$ is the sample size. Without specifying a confidence level, we assume the standard 95% confidence level, so $z = 1.96$, $p = 0.25$, and $n = 602$. Plugging these values into the formula gives $ME = 1.96 \times \sqrt{\frac{0.25(1-0.25)}{602}} \approx 0.041$.

Question 11

Use the 68-95-99.7 rule to solve the problem.
-The amount of Jen's monthly phone bill is normally distributed with a mean of $70 and a standard deviation of $9. What percentage of her phone bills are between $43 and $97?
A)68%
B)95%
C)99.9%
D)99.7%

Accepted Answer

The 68-95-99.7 rule, also known as the empirical rule, states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations. The range from $43 to $97 is $27 below and above the mean ($70), which is exactly three standard deviations ($9 * 3 = $27). Therefore, approximately 99.7% of Jen's phone bills are between $43 and $97.

Question 12

Identify the distribution as symmetric, left-skewed, or right-skewed.
-Shoe sizes of adult women
A)Right-skewed
B)Left-skewed
C)Symmetric

Accepted Answer

The distribution of shoe sizes for adult women tends to be symmetric, as there is a common average size around which sizes are evenly distributed, with fewer women having very small or very large sizes.

Question 13

Find the standard deviation for the given data. Round your answer to one more decimal place than the original data.
-$\begin{array} { l l l l l l l } 40 & 20 & 37 & 20 & 17 & 49 & 72 \end{array}$
A) 37
B) $19.8$
C) $9289.3$
D) 11,643

Accepted Answer

The standard deviation is calculated by finding the square root of the variance. First, find the mean of the data: $(40 + 20 + 37 + 20 + 17 + 49 + 72) / 7 = 255 / 7 = 36.43$. Then, calculate the variance by finding the sum of the squared differences from the mean, divided by the number of data points: $((40-36.43)^2 + (20-36.43)^2 + (37-36.43)^2 + (20-36.43)^2 + (17-36.43)^2 + (49-36.43)^2 + (72-36.43)^2) / 7 = 392.86$. The standard deviation is the square root of the variance: $\sqrt{392.86} \approx 19.8$.

Question 14

Use the range rule of thumb to approximate the standard deviation.
-The maximum value of a distribution is 18.1 and the minimum value is 5.5. Round results to the nearest tenth.
A)14.2
B)3.2
C)0.2
D)8.2

Accepted Answer

The range rule of thumb for estimating the standard deviation is to divide the range of the distribution by 4. The range is the maximum value minus the minimum value, which is 18.1 - 5.5 = 12.6. Dividing this by 4 gives 12.6 / 4 = 3.15, which rounds to 3.2.

Question 15

State whether you think the difference between what occurred and what you would expect by chance is statisticallysignificant.
-At Linden High School there are math tests at the end of each three-month session. On all of the last 10 days when there was a math test at school, Brian got a cold and had to stay home. He didn't
Have colds at other times.
A)Statistically significant
B)Not statistically significant

Accepted Answer

The coincidence of Brian getting a cold on all 10 days of math tests and not at other times suggests a pattern that is unlikely to occur by chance alone, indicating statistical significance.

Question 16

Identify the distribution as symmetric, left-skewed, or right-skewed.
-Number of days worked last year by adult males in a U.S. city which has a low unemployment rate
A)Symmetric
B)Right-skewed
C)Left-skewed

Accepted Answer

Given the context of a low unemployment rate, most adult males would have worked close to the maximum number of days in a year, with fewer individuals working significantly less. This scenario leads to a distribution where the tail is longer on the left side, indicating left-skewness.

Question 17

Find the range for the given data.
-The manager of an electrical supply store measured the diameters of the rolls of wire in the inventory. The diameters of the rolls (in m)are listed below. 
$\begin{array} { l } 
0.519 \
0.599 \
0.137 \
0.341 \
0.335 \
0.118
\end{array}$
A) $0.118 \mathrm {~m}$
B) $0.519 \mathrm {~m}$
C) $0.198 \mathrm {~m}$
D) $0.481 \mathrm {~m}$

Accepted Answer

The range of a set of data is the difference between the highest and lowest values in the set. In this case, the highest value is 0.599 m and the lowest is 0.118 m. Subtracting these gives 0.599 - 0.118 = 0.481 m, which is the range.

Question 18

Construct a boxplot as requested.
-The normal monthly precipitation (in inches)for August is listed for 20 different U.S. cities. Construct a boxplot for the data set. $\begin{array} { l l l l l } 4.0 & 1.0 & 1.5 & 1.6 & 2.0 \end{array}$
$\begin{array} { l l l l l } 2.2 & 2.4 & 2.7 & 3.4 & 3.4 \ 3.5 & 3.6 & 3.6 & 3.7 & 3.7 \end{array}$
$\begin{array} { l l l l l l } 3.5 & 3.6 & 3.6 & 3.7 & 3.7 \ 3.9 & 4.1 & 4.2 & 4.2 & 7.0 \end{array}$
$\begin{array} { l l l l l l } 3.9 & 4.1 & 4.2 & 4.2 & 7.0 \end{array}$
A)

B)

C)

D)

Accepted Answer

The answer of Construct a boxplot as requested.
-The normal monthly...

Question 19

Identify the distribution as symmetric, left-skewed, or right-skewed.
-Lengths of human pregnancies
A)Right-skewed
B)Left-skewed
C)Symmetric

Accepted Answer

The distribution of lengths of human pregnancies is generally symmetric, as most pregnancies last around 40 weeks, with fewer cases of significantly shorter or longer durations.

Question 20

Find the median for the given sample data.
-The salaries of ten randomly selected doctors are shown below. $$\begin{array} { l l l l l } 
\$ 111,000 & \$ 129,000 & \$ 198,000 & \$ 228,000 & \$ 223,000 \
\$ 131,000 & \$ 110,000 & \$ 714,000 & \$ 241,000 & \$ 170,000
\end{array}$$
Find the median salary.
A) $\$ 251,000$
B) $\$ 226,000$
C) $\$ 184,000$
D) $\$ 198,000$

Accepted Answer

To find the median, first, arrange the salaries in ascending order: $110,000, $111,000, $129,000, $131,000, $170,000, $198,000, $223,000, $228,000, $241,000, $714,000. With ten numbers, the median is the average of the 5th and 6th numbers: ($170,000 + $198,000) / 2 = $368,000 / 2 = $184,000.

Quiz 6: Putting Statistics to Work

State whether you would expect the data set to be normally distributed. -Amount of credit card debt of families in the U.S.

State whether you think the difference between what occurred and what you would expect by chance is statisticallysignificant. -There are two candidates for mayor, Maria Hernandez, and Eric Wong. Of 100 people polled, 53 say they will vote for Maria Hernandez.

State whether you would expect the data set to be normally distributed. -The diameters of the redwood trees in a forest.

For the given data value, find the standard score and the percentile. -A data value $1.3$ standard deviations above the mean.

State whether the distribution appears to be (roughly) normal. -

Use the 68-95-99.7 rule to solve the problem. -At one college, GPA's are normally distributed with a mean of 3 and a standard deviation of 0.6. What percentage of students at the college have a GPA between 2.4 and 3.6?

Find the margin of error for the survey results described. -In a survey of 602 employees of a large company, 25% said that they had high job satisfaction. Give your answer as a decimal to three decimal places.

Use the 68-95-99.7 rule to solve the problem. -The amount of Jen's monthly phone bill is normally distributed with a mean of $70 and a standard deviation of $9. What percentage of her phone bills are between $43 and $97?

Identify the distribution as symmetric, left-skewed, or right-skewed. -Shoe sizes of adult women

Find the standard deviation for the given data. Round your answer to one more decimal place than the original data. - $\begin{array} { l l l l l l l } 40 & 20 & 37 & 20 & 17 & 49 & 72 \end{array}$

Use the range rule of thumb to approximate the standard deviation. -The maximum value of a distribution is 18.1 and the minimum value is 5.5. Round results to the nearest tenth.

Identify the distribution as symmetric, left-skewed, or right-skewed. -Number of days worked last year by adult males in a U.S. city which has a low unemployment rate

Find the range for the given data. -The manager of an electrical supply store measured the diameters of the rolls of wire in the inventory. The diameters of the rolls (in m) are listed below. $\begin{array} { l } 0.519 \\0.599 \\0.137 \\0.341 \\0.335 \\0.118\end{array}$

Identify the distribution as symmetric, left-skewed, or right-skewed. -Lengths of human pregnancies

Find the median for the given sample data. -The salaries of ten randomly selected doctors are shown below. $\begin{array} { l l l l l } \$ 111,000 & \$ 129,000 & \$ 198,000 & \$ 228,000 & \$ 223,000 \\\$ 131,000 & \$ 110,000 & \$ 714,000 & \$ 241,000 & \$ 170,000\end{array}$ Find the median salary.