QuestionFind the percentile of 7.1 lbs, calculate $Q_{1}, Q_{2}, Q_{3}$ , create a box plot, and analyze its skewness. Also, find binomial probabilities for 4 and at least 6 out of 7 adults enjoying superhero movies.

Studdy Solution

STEP 1

Assumptions1. The weights of30 newborn babies are given. The weights are listed in ascending order3. We are asked to find the percentile of7.1 pounds, the weight in the39th percentile, the first quartile (Q1), the second quartile (Q), the third quartile (Q3), and to construct a box plot and determine its skewness.

STEP 2

First, we need to find the percentile of7.1 pounds. The percentile of a value is the percentage of values in a data set that are less than or equal to that value. $Percentile = \frac{Number\, of\, values\, less\, than\, or\, equal\, to\, the\, given\, value}{Total\, number\, of\, values} \times100$

STEP 3

Now, plug in the given values for the number of values less than or equal to7.1 and the total number of values to calculate the percentile.
$Percentile = \frac{18}{30} \times100$

STEP 4

Calculate the percentile of7.1 pounds.
$Percentile = \frac{18}{30} \times100 =60$ The7.1 pounds is in the60th percentile.

STEP 5

Next, we need to find the weight in the39th percentile. To do this, we multiply the percentile by the total number of values and round to the nearest whole number. This gives us the index of the value in the39th percentile.
$Index = Round(Percentile \times Total\, number\, of\, values)$

STEP 6

Now, plug in the given values for the percentile and the total number of values to calculate the index.
$Index = Round(0.39 \times30)$

STEP 7

Calculate the index.
$Index = Round(0.39 \times30) =12$

STEP 8

The weight in the39th percentile is the12th value in the sorted list, which is6.7 pounds.

STEP 9

Next, we need to find the first quartile (Q), the second quartile (Q2), and the third quartile (Q3). The first quartile is the median of the lower half of the data, the second quartile is the median of the entire data set, and the third quartile is the median of the upper half of the data.

STEP 10

To find Q, we take the median of the first15 values. This is the8th value in the sorted list, which is6.4 pounds.

STEP 11

To find Q, we take the median of all30 values. This is the average of the15th and16th values in the sorted list, which is (7.0 +7.0) / =7.0 pounds.

STEP 12

To find Q, we take the median of the last15 values. This is the23rd value in the sorted list, which is7.7 pounds.

STEP 13

To construct a box plot, we need the minimum value, Q, Q2, Q3, and the maximum value. The minimum value is5.5 pounds, the maximum value is8.7 pounds, and we have already calculated Q, Q2, and Q3.

STEP 14

The box plot is constructed with the box extending from Q to Q3, a line at Q2 (the median), and whiskers extending from the box to the minimum and maximum values.

STEP 15

To determine the skewness of the box plot, we look at the lengths of the whiskers and the position of the median. If the right whisker is longer than the left whisker and the median is closer to the left side of the box, the box plot is right skewed. If the left whisker is longer than the right whisker and the median is closer to the right side of the box, the box plot is left skewed. If the whiskers are approximately the same length and the median is in the middle of the box, the box plot is symmetric.

STEP 16

In this case, the right whisker is longer than the left whisker and the median is closer to the left side of the box, so the box plot is right skewed.

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QuestionFind the percentile of 7.1 lbs, calculate $Q_{1}, Q_{2}, Q_{3}$ , create a box plot, and analyze its skewness. Also, find binomial probabilities for 4 and at least 6 out of 7 adults enjoying superhero movies.

Studdy Solution

STEP 1

STEP 2

First, we need to find the percentile of7.1 pounds. The percentile of a value is the percentage of values in a data set that are less than or equal to that value. $Percentile = \frac{Number\, of\, values\, less\, than\, or\, equal\, to\, the\, given\, value}{Total\, number\, of\, values} \times100$

STEP 3

Now, plug in the given values for the number of values less than or equal to7.1 and the total number of values to calculate the percentile.
$Percentile = \frac{18}{30} \times100$

STEP 4

Calculate the percentile of7.1 pounds.
$Percentile = \frac{18}{30} \times100 =60$ The7.1 pounds is in the60th percentile.

STEP 5

Next, we need to find the weight in the39th percentile. To do this, we multiply the percentile by the total number of values and round to the nearest whole number. This gives us the index of the value in the39th percentile.
$Index = Round(Percentile \times Total\, number\, of\, values)$

STEP 6

Now, plug in the given values for the percentile and the total number of values to calculate the index.
$Index = Round(0.39 \times30)$

STEP 7

Calculate the index.
$Index = Round(0.39 \times30) =12$

STEP 8

The weight in the39th percentile is the12th value in the sorted list, which is6.7 pounds.

STEP 9

Next, we need to find the first quartile (Q), the second quartile (Q2), and the third quartile (Q3). The first quartile is the median of the lower half of the data, the second quartile is the median of the entire data set, and the third quartile is the median of the upper half of the data.

STEP 10

To find Q, we take the median of the first15 values. This is the8th value in the sorted list, which is6.4 pounds.

STEP 11

To find Q, we take the median of all30 values. This is the average of the15th and16th values in the sorted list, which is (7.0 +7.0) / =7.0 pounds.

STEP 12

To find Q, we take the median of the last15 values. This is the23rd value in the sorted list, which is7.7 pounds.

STEP 13

To construct a box plot, we need the minimum value, Q, Q2, Q3, and the maximum value. The minimum value is5.5 pounds, the maximum value is8.7 pounds, and we have already calculated Q, Q2, and Q3.

STEP 14

The box plot is constructed with the box extending from Q to Q3, a line at Q2 (the median), and whiskers extending from the box to the minimum and maximum values.

STEP 15

STEP 16

In this case, the right whisker is longer than the left whisker and the median is closer to the left side of the box, so the box plot is right skewed.

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QuestionFind the percentile of 7.1 lbs, calculate Q1,Q2,Q3Q_{1}, Q_{2}, Q_{3}Q1​,Q2​,Q3​, create a box plot, and analyze its skewness. Also, find binomial probabilities for 4 and at least 6 out of 7 adults enjoying superhero movies.

Studdy Solution

STEP 1

STEP 2

STEP 3

Now, plug in the given values for the number of values less than or equal to7.1 and the total number of values to calculate the percentile.Percentile=1830×100Percentile = \frac{18}{30} \times100Percentile=3018​×100

STEP 4

Calculate the percentile of7.1 pounds.Percentile=1830×100=60Percentile = \frac{18}{30} \times100 =60Percentile=3018​×100=60The7.1 pounds is in the60th percentile.

STEP 5

STEP 6

Now, plug in the given values for the percentile and the total number of values to calculate the index.Index=Round(0.39×30)Index = Round(0.39 \times30)Index=Round(0.39×30)

STEP 7

Calculate the index.Index=Round(0.39×30)=12Index = Round(0.39 \times30) =12Index=Round(0.39×30)=12

STEP 8

The weight in the39th percentile is the12th value in the sorted list, which is6.7 pounds.

STEP 9

Next, we need to find the first quartile (Q), the second quartile (Q2), and the third quartile (Q3). The first quartile is the median of the lower half of the data, the second quartile is the median of the entire data set, and the third quartile is the median of the upper half of the data.

STEP 10

To find Q, we take the median of the first15 values. This is the8th value in the sorted list, which is6.4 pounds.

STEP 11

To find Q, we take the median of all30 values. This is the average of the15th and16th values in the sorted list, which is (7.0 +7.0) / =7.0 pounds.

STEP 12

To find Q, we take the median of the last15 values. This is the23rd value in the sorted list, which is7.7 pounds.

STEP 13

To construct a box plot, we need the minimum value, Q, Q2, Q3, and the maximum value. The minimum value is5.5 pounds, the maximum value is8.7 pounds, and we have already calculated Q, Q2, and Q3.

STEP 14

The box plot is constructed with the box extending from Q to Q3, a line at Q2 (the median), and whiskers extending from the box to the minimum and maximum values.

STEP 15

STEP 16

In this case, the right whisker is longer than the left whisker and the median is closer to the left side of the box, so the box plot is right skewed.

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QuestionFind the percentile of 7.1 lbs, calculate $Q_{1}, Q_{2}, Q_{3}$ , create a box plot, and analyze its skewness. Also, find binomial probabilities for 4 and at least 6 out of 7 adults enjoying superhero movies.

Now, plug in the given values for the number of values less than or equal to7.1 and the total number of values to calculate the percentile.
$Percentile = \frac{18}{30} \times100$

Calculate the percentile of7.1 pounds.
$Percentile = \frac{18}{30} \times100 =60$ The7.1 pounds is in the60th percentile.

Now, plug in the given values for the percentile and the total number of values to calculate the index.
$Index = Round(0.39 \times30)$

Calculate the index.
$Index = Round(0.39 \times30) =12$