Answer: the probability that she will be between 65 and 67 inches tall is 0.2077
Step-by-step explanation:
Since heights of women in the United States are normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = heights of women.
µ = mean height
σ = standard deviation
From the information given,
µ = 63.7 inches
σ = 2.7 inches
We want to find the probability that the height of a woman selected will be between 65 and 67 inches. It is expressed as
P(65 ≤ x ≤ 67)
For x = 65,
z = (65 - 63.75)/2.7 = 0.46
Looking at the normal distribution table, the probability corresponding to the z score is 0.6772
For x = 67,
z = (67 - 63.75)/2.7 = 1.2
Looking at the normal distribution table, the probability corresponding to the z score is 0.8849
P(65 ≤ x ≤ 67) = 0.8849 - 0.6772
= 0.2077
This would be a rational number. Rational numbers are numbers that can be written as fractions. 1.68 = 168/100
Answer:
a) m∠BPD = 120°
b) m∠BC + m∠AD = 120°
Step-by-step explanation:
a) To solve for question a, we make use of a theorem called the intersecting chord theorem. This states that:
The measure of the angle formed by two chords that intersect inside a circle is the average of the measures of the intercepted arcs.
The Interior angle =( The larger exterior arc + The smaller exterior arcs) ÷ 2
The larger exterior arc (m∠BD) = 170°
The small exterior arc (m∠CA) = 70°
m∠BPD = m∠BD + m∠CA/2
m∠BPD = 170° + 70°/2
= 240°/2
= 120°
b) We are to find m∠BC + m∠AD
The sum of exterior angles in a circle = 360°
360° = m∠BD + m∠CA + m∠BC + m∠AD
360° = 170° + 70° + m∠BC + m∠AD
360° = 240 + m∠BC + m∠AD
360 - 240° = m∠BC + m∠AD
Thererefore,
m∠BC + m∠AD = 120°
This is called the <u>Multiplication property of equality.</u>
The multiplication property of equality states that whatever you multiply on one side, you must multiply the same quantity on the other side of the equation. In this case, variable c is multiplied to both sides of the equation.