Answer:
a) 0.283 or 28.3%
b) 0.130 or 13%
c) 0.4 or 40%
d) 30.6 mm
Step-by-step explanation:
z-score of a single left atrial diameter value of healthy children can be calculated as:
z=
where
- X is the left atrial diameter value we are looking for its z-score
- M is the mean left atrial diameter of healthy children (26.7 mm)
- s is the standard deviation (4.7 mm)
Then
a) proportion of healthy children who have left atrial diameters less than 24 mm
=P(z<z*) where z* is the z-score of 24 mm
z*=
≈ −0.574
And P(z<−0.574)=0.283
b) proportion of healthy children who have left atrial diameters greater than 32 mm
= P(z>z*) = 1-P(z<z*) where z* is the z-score of 32 mm
z*=
≈ 1.128
1-P(z<1.128)=0.8703=0.130
c) proportion of healthy children have left atrial diameters between 25 and 30 mm
=P(z(25)<z<z(30)) where z(25), z(30) are the z-scores of 25 and 30 mm
z(30)=
≈ 0.702
z(25)=
≈ −0.362
P(z<0.702)=0.7587
P(z<−0.362)=0.3587
Then P(z(25)<z<z(30)) =0.7587 - 0.3587 =0.4
d) to find the value for which only about 20% have a larger left atrial diameter, we assume
P(z>z*)=0.2 or 20% where z* is the z-score of the value we are looking for.
Then P(z<z*)=0.8 and z*=0.84. That is
0.84=
solving this equation for X we get X=30.648
The mixed number as an improper fraction is 37/8
<h3>How to express the mixed number as an improper fraction?</h3>
The diameter is give as:
Diameter = 4 5/8
Next we convert the above number to an improper fraction
The numerator is calculated as
Numerator = 8 * 4 + 5
This gives
Numerator = 37
Hence, the mixed number as an improper fraction is 37/8
Read more about fractions at:
brainly.com/question/18734292
#SPJ1
Step-by-step explanation:
Use the form (a + b)(a - b) = a^2 - b^2:
(2x^4 + 3x^3)(2x^4 - 3x^3) = 4x^8 - 9x^6.
2x - (3x + 2x)
= -3x
hope this helps !!
40.7..........................