Solved on Mar 05, 2024

Rewrite the confidence interval $0.22 < p < 0.72$ using plus/minus notation and interval notation.
(a) plus/minus notation: $p = 0.47 \pm 0.25$ (b) interval notation: $(0.22, 0.72)$

STEP 1

Assumptions
1. The given confidence interval is $0.22 < p < 0.72$ .
2. We need to rewrite this interval in two different notations: plus/minus notation and interval notation.

STEP 2

To express the confidence interval in plus/minus notation, we need to find the midpoint of the interval. The midpoint is the average of the lower and upper bounds of the interval.
$Midpoint = \frac{Lower\, bound + Upper\, bound}{2}$

STEP 3

Now, plug in the given values for the lower bound ( $0.22$ ) and the upper bound ( $0.72$ ) to calculate the midpoint.
$Midpoint = \frac{0.22 + 0.72}{2}$

STEP 4

Calculate the midpoint.
$Midpoint = \frac{0.22 + 0.72}{2} = \frac{0.94}{2} = 0.47$

STEP 5

Next, we need to find the distance from the midpoint to either bound of the interval, which will be the "plus/minus" value.
$Plus/Minus\, value = Upper\, bound - Midpoint$

STEP 6

Plug in the values for the upper bound ( $0.72$ ) and the midpoint ( $0.47$ ) to calculate the "plus/minus" value.
$Plus/Minus\, value = 0.72 - 0.47$

STEP 7

Calculate the "plus/minus" value.
$Plus/Minus\, value = 0.72 - 0.47 = 0.25$

STEP 8

Now we can write the confidence interval in plus/minus notation using the midpoint and the "plus/minus" value.
$p = Midpoint \pm Plus/Minus\, value$

STEP 9

Plug in the values for the midpoint ( $0.47$ ) and the "plus/minus" value ( $0.25$ ) to express the confidence interval in plus/minus notation.
$p = 0.47 \pm 0.25$

STEP 10

For interval notation, we simply need to express the interval as a pair of numbers enclosed in parentheses, representing the lower and upper bounds.
$Interval\, notation = (Lower\, bound, Upper\, bound)$

STEP 11

Plug in the values for the lower bound ( $0.22$ ) and the upper bound ( $0.72$ ) to express the confidence interval in interval notation.
$Interval\, notation = (0.22, 0.72)$
The confidence interval $0.22 < p < 0.72$ can be rewritten as: (a) plus/minus notation: $p = 0.47 \pm 0.25$ (b) interval notation: $(0.22, 0.72)$

Was this helpful?

Rewrite the confidence interval $0.22 < p < 0.72$ using plus/minus notation and interval notation.
(a) plus/minus notation: $p = 0.47 \pm 0.25$ (b) interval notation: $(0.22, 0.72)$

STEP 1

Assumptions
1. The given confidence interval is $0.22 < p < 0.72$ .
2. We need to rewrite this interval in two different notations: plus/minus notation and interval notation.

STEP 2

To express the confidence interval in plus/minus notation, we need to find the midpoint of the interval. The midpoint is the average of the lower and upper bounds of the interval.
$Midpoint = \frac{Lower\, bound + Upper\, bound}{2}$

STEP 3

Now, plug in the given values for the lower bound ( $0.22$ ) and the upper bound ( $0.72$ ) to calculate the midpoint.
$Midpoint = \frac{0.22 + 0.72}{2}$

STEP 4

Calculate the midpoint.
$Midpoint = \frac{0.22 + 0.72}{2} = \frac{0.94}{2} = 0.47$

STEP 5

Next, we need to find the distance from the midpoint to either bound of the interval, which will be the "plus/minus" value.
$Plus/Minus\, value = Upper\, bound - Midpoint$

STEP 6

Plug in the values for the upper bound ( $0.72$ ) and the midpoint ( $0.47$ ) to calculate the "plus/minus" value.
$Plus/Minus\, value = 0.72 - 0.47$

STEP 7

Calculate the "plus/minus" value.
$Plus/Minus\, value = 0.72 - 0.47 = 0.25$

STEP 8

Now we can write the confidence interval in plus/minus notation using the midpoint and the "plus/minus" value.
$p = Midpoint \pm Plus/Minus\, value$

STEP 9

Plug in the values for the midpoint ( $0.47$ ) and the "plus/minus" value ( $0.25$ ) to express the confidence interval in plus/minus notation.
$p = 0.47 \pm 0.25$

STEP 10

For interval notation, we simply need to express the interval as a pair of numbers enclosed in parentheses, representing the lower and upper bounds.
$Interval\, notation = (Lower\, bound, Upper\, bound)$

STEP 11

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Rewrite the confidence interval 0.22<p<0.720.22 < p < 0.720.22<p<0.72 using plus/minus notation and interval notation.(a) plus/minus notation: p=0.47±0.25p = 0.47 \pm 0.25p=0.47±0.25 (b) interval notation: (0.22,0.72)(0.22, 0.72)(0.22,0.72)

STEP 1

Assumptions1. The given confidence interval is 0.22<p<0.720.22 < p < 0.720.22<p<0.72.2. We need to rewrite this interval in two different notations: plus/minus notation and interval notation.

STEP 2

To express the confidence interval in plus/minus notation, we need to find the midpoint of the interval. The midpoint is the average of the lower and upper bounds of the interval.Midpoint=Lower bound+Upper bound2Midpoint = \frac{Lower\, bound + Upper\, bound}{2}Midpoint=2Lowerbound+Upperbound​

STEP 3

Now, plug in the given values for the lower bound (0.220.220.22) and the upper bound (0.720.720.72) to calculate the midpoint.Midpoint=0.22+0.722Midpoint = \frac{0.22 + 0.72}{2}Midpoint=20.22+0.72​

STEP 4

Calculate the midpoint.Midpoint=0.22+0.722=0.942=0.47Midpoint = \frac{0.22 + 0.72}{2} = \frac{0.94}{2} = 0.47Midpoint=20.22+0.72​=20.94​=0.47

STEP 5

Next, we need to find the distance from the midpoint to either bound of the interval, which will be the "plus/minus" value.Plus/Minus value=Upper bound−MidpointPlus/Minus\, value = Upper\, bound - MidpointPlus/Minusvalue=Upperbound−Midpoint

STEP 6

Plug in the values for the upper bound (0.720.720.72) and the midpoint (0.470.470.47) to calculate the "plus/minus" value.Plus/Minus value=0.72−0.47Plus/Minus\, value = 0.72 - 0.47Plus/Minusvalue=0.72−0.47

STEP 7

Calculate the "plus/minus" value.Plus/Minus value=0.72−0.47=0.25Plus/Minus\, value = 0.72 - 0.47 = 0.25Plus/Minusvalue=0.72−0.47=0.25

STEP 8

Now we can write the confidence interval in plus/minus notation using the midpoint and the "plus/minus" value.p=Midpoint±Plus/Minus valuep = Midpoint \pm Plus/Minus\, valuep=Midpoint±Plus/Minusvalue

STEP 9

Plug in the values for the midpoint (0.470.470.47) and the "plus/minus" value (0.250.250.25) to express the confidence interval in plus/minus notation.p=0.47±0.25p = 0.47 \pm 0.25p=0.47±0.25

STEP 10

For interval notation, we simply need to express the interval as a pair of numbers enclosed in parentheses, representing the lower and upper bounds.Interval notation=(Lower bound,Upper bound)Interval\, notation = (Lower\, bound, Upper\, bound)Intervalnotation=(Lowerbound,Upperbound)

STEP 11

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Rewrite the confidence interval $0.22 < p < 0.72$ using plus/minus notation and interval notation.
(a) plus/minus notation: $p = 0.47 \pm 0.25$ (b) interval notation: $(0.22, 0.72)$

Assumptions
1. The given confidence interval is $0.22 < p < 0.72$ .
2. We need to rewrite this interval in two different notations: plus/minus notation and interval notation.

To express the confidence interval in plus/minus notation, we need to find the midpoint of the interval. The midpoint is the average of the lower and upper bounds of the interval.
$Midpoint = \frac{Lower\, bound + Upper\, bound}{2}$

Now, plug in the given values for the lower bound ( $0.22$ ) and the upper bound ( $0.72$ ) to calculate the midpoint.
$Midpoint = \frac{0.22 + 0.72}{2}$

Calculate the midpoint.
$Midpoint = \frac{0.22 + 0.72}{2} = \frac{0.94}{2} = 0.47$

Next, we need to find the distance from the midpoint to either bound of the interval, which will be the "plus/minus" value.
$Plus/Minus\, value = Upper\, bound - Midpoint$

Plug in the values for the upper bound ( $0.72$ ) and the midpoint ( $0.47$ ) to calculate the "plus/minus" value.
$Plus/Minus\, value = 0.72 - 0.47$

Calculate the "plus/minus" value.
$Plus/Minus\, value = 0.72 - 0.47 = 0.25$

Now we can write the confidence interval in plus/minus notation using the midpoint and the "plus/minus" value.
$p = Midpoint \pm Plus/Minus\, value$

Plug in the values for the midpoint ( $0.47$ ) and the "plus/minus" value ( $0.25$ ) to express the confidence interval in plus/minus notation.
$p = 0.47 \pm 0.25$

For interval notation, we simply need to express the interval as a pair of numbers enclosed in parentheses, representing the lower and upper bounds.
$Interval\, notation = (Lower\, bound, Upper\, bound)$