Answer:
Z scores of -2 or lower are considered unusually low. Since the z-score of a 49-cm head circunference is -2, it is an unusual measure.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean
and standard deviation
, the zscore of a measure X is given by:
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Z scores of -2 or lower are considered unusually low, and zscores of 2 or higher are considered unusually high.
In this problem, we have that:
![\mu = 55, \sigma = 3](https://tex.z-dn.net/?f=%5Cmu%20%3D%2055%2C%20%5Csigma%20%3D%203)
49cm head circunference unusual?
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![Z = \frac{49 - 55}{3}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B49%20-%2055%7D%7B3%7D)
![Z = -2](https://tex.z-dn.net/?f=Z%20%3D%20-2)
Z scores of -2 or lower are considered unusually low. Since the z-score of a 49-cm head circunference is -2, it is an unusual measure.
Answer:
![\mu = 367](https://tex.z-dn.net/?f=%5Cmu%20%3D%20367)
![\sigma = 88](https://tex.z-dn.net/?f=%5Csigma%20%3D%2088)
a. What is the probability that the cost will be more than $450?
We are supposed to find P(x > 450)
Formula : ![z=\frac{x-\mu}{\sigma}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D)
![z=\frac{450-367}{88}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7B450-367%7D%7B88%7D)
![z=0.9431](https://tex.z-dn.net/?f=z%3D0.9431)
Refer the z table :
P(z<0.9431)=0.8264
P(z> 0.9431)=1-P(z<0.9431)=1- 0.8264= 0.1736
Hence the probability that the cost will be more than $450 is 0.1736
b)What is the probability that the cost will be less than $250?
We are supposed to find P(x<250)
Formula : ![z=\frac{x-\mu}{\sigma}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D)
![z=\frac{250-367}{88}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7B250-367%7D%7B88%7D)
![z=-1.3295](https://tex.z-dn.net/?f=z%3D-1.3295)
Refer the z table :
P(z<-1.3295)=0.0934
Hence the probability that the cost will be less than $250 is 0.0934
c)What is the probability that the cost will be between $250 and $450?
P(250<z<450)=P(z<450)-P(z<250) = 0.8264 - 0.0934 =0.733
Hence the probability that the cost will be between $250 and $450 is 0.733
d) If the cost for your car repair is in the lower 5% of automobile repair charges, what is your cost?
p = 0.05
refer the z table
z = -1.65
Formula : ![z=\frac{x-\mu}{\sigma}](https://tex.z-dn.net/?f=z%3D%5Cfrac%7Bx-%5Cmu%7D%7B%5Csigma%7D)
![-1.65=\frac{x-367}{88}](https://tex.z-dn.net/?f=-1.65%3D%5Cfrac%7Bx-367%7D%7B88%7D)
![-1.65 \times 88=x-367](https://tex.z-dn.net/?f=-1.65%20%5Ctimes%2088%3Dx-367)
![-145.2+367=x](https://tex.z-dn.net/?f=-145.2%2B367%3Dx)
![221.8=x](https://tex.z-dn.net/?f=221.8%3Dx)
Hence If the cost for your car repair is in the lower 5% of automobile repair charges, so, cost is $221.8
AB = AX+XB = 6+18 = 24
The ratio of AB to AX is AB/AX = 24/6 = 4
AC = AY+YC = 10+25 = 35
The ratio of AC to AY is AC/AY = 25/10 = 3.5
The results of each division are 4 and 3.5
We do <u>not</u> get the same result, which means that the proportion
is <u>not</u> true. This is sufficient to prove that the triangles aren't similar. We need them to be in proportion so that we can use the SAS similarity rule.
<h3>Answer: The triangles aren't similar</h3>
Answer:
A 9 pound package will cost $20.
Step-by-step explanation:
Let p be the number of extra pounds (after 5).
Cost = $8 + 3p
So $8 + 3*4 = $20
Answer:
The photo above show you how to graph it.
The equation is y=2x-3
Step-by-step explanation:
Hope this helped