Complete Question
The complete question is shown on the first uploaded image
Answer:
a
![P(X < 65) = 0.003467](https://tex.z-dn.net/?f=P%28X%20%3C%2065%29%20%3D%20%200.003467)
b
c
![P(X > 120 ) =0.062024](https://tex.z-dn.net/?f=P%28X%20%3E%20120%20%29%20%3D0.062024)
Step-by-step explanation:
From the question we are told that
The mean is ![\mu = \$ 100](https://tex.z-dn.net/?f=%5Cmu%20%20%3D%20%20%5C%24%20100)
The standard deviation is ![\sigma = \$ 13](https://tex.z-dn.net/?f=%5Csigma%20%20%3D%20%20%5C%24%2013)
Generally the probability that the monthly utility bills is less than $65 is mathematically represented as
![P(X < 65) = P(\frac{X - \mu }{\sigma } < \frac{65 - 100 }{13 } )](https://tex.z-dn.net/?f=P%28X%20%3C%2065%29%20%3D%20%20P%28%5Cfrac%7BX%20%20-%20%20%5Cmu%20%7D%7B%5Csigma%20%7D%20%20%3C%20%5Cfrac%7B65%20%20-%20%20100%20%7D%7B13%20%7D%20%20%20%29)
Generally
![\frac{X - \mu }{\sigma } = Z (The\ standardized \ value \ of\ X )](https://tex.z-dn.net/?f=%5Cfrac%7BX%20%20-%20%20%5Cmu%20%7D%7B%5Csigma%20%7D%20%3D%20%20Z%20%28The%5C%20standardized%20%5C%20value%20%5C%20of%5C%20%20X%20%29)
So
![P(X < 65) = P(Z < -2.70 )](https://tex.z-dn.net/?f=P%28X%20%3C%2065%29%20%3D%20%20P%28Z%20%3C%20-2.70%20%20%29)
From the z-table
![P(Z < -2.70 ) = 0.003467](https://tex.z-dn.net/?f=P%28Z%20%3C%20-2.70%20%20%29%20%3D%20%200.003467)
So
![P(X < 65) = 0.003467](https://tex.z-dn.net/?f=P%28X%20%3C%2065%29%20%3D%20%200.003467)
Generally the probability that a randomly selected utility bill is between $86 and $110 is mathematically represented as
![P(86 < X< 110 )= P( \frac{86 -100}{ 13} < \frac{X - \mu}{\sigma } < \frac{86 -100}{ 13} )](https://tex.z-dn.net/?f=P%2886%20%3C%20%20X%3C%20%20110%20%29%3D%20%20P%28%20%5Cfrac%7B86%20-100%7D%7B%2013%7D%20%3C%20%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%20%7D%20%3C%20%5Cfrac%7B86%20-100%7D%7B%2013%7D%20%20%20%20%29)
=>
=>
=>
From the z-table
![P(Z < 0.77 ) = 0.77935](https://tex.z-dn.net/?f=P%28Z%20%3C%200.77%20%29%20%3D%200.77935)
and
![P(Z < -1.08 ) = 0.14007](https://tex.z-dn.net/?f=P%28Z%20%3C%20-1.08%20%29%20%3D%20%200.14007)
So
=>
Generally the probability that the monthly utility bills is more than $120 is mathematically represented as
![P(X >120 ) = P(\frac{X - \mu }{\sigma } > \frac{120 - 100 }{13 })](https://tex.z-dn.net/?f=P%28X%20%3E120%20%29%20%3D%20%20P%28%5Cfrac%7BX%20%20-%20%20%5Cmu%20%7D%7B%5Csigma%20%7D%20%20%3E%20%5Cfrac%7B120%20%20-%20%20100%20%7D%7B13%20%7D%29)
=> ![P(X > 120 ) = P(Z > 1.538 )](https://tex.z-dn.net/?f=P%28X%20%3E%20120%20%29%20%3D%20%20P%28Z%20%3E%201.538%20%20%20%29)
From the z-table
![P(Z > 1.54 ) = 0.062024](https://tex.z-dn.net/?f=P%28Z%20%3E%201.54%20%20%29%20%3D%20%200.062024)
So
![P(X > 120 ) =0.062024](https://tex.z-dn.net/?f=P%28X%20%3E%20120%20%29%20%3D0.062024)
Answer:
142 km^3
Step-by-step explanation:
A=2(wl+hl+hw)
A=2(7*5+3*5+3*7)
A=142
Answer: 15 : 16
<u>Step-by-step explanation:</u>
x : y y : z
3 : 1 4 : 3
Find the LCM for both y's. LCM = 4
x : y y : z
3(4) : 1(4) 4 : 3
12 : 4 4 : 3
--> x : y : z = 12 : 4 : 3
(x + z) : (x + y)
12 + 3 : 12 + 4
15 : 16
By completing the experiment a few more times and combining the results to the trails already done
Hope this helps you!! xD
The percentage of tardiness among the 102 pupils is 2.94.
<h2>Calculation of the percentage</h2>
According to the query,
Course A: Total number of students = 102
Number of tardy students = 3
Percent of students tardy in course A = (number of tardy students/total
number of students) * 100
=(3/102)*100
= 2.941
≈2.94
In case of course B: Total number of students = 85 & tardy student = 5
So, the percent of tardy student = (5/85)*100 = 5.88 %
Therefore, it is concluded that the percentage of student tardiness in course A is 2.94.
Learn more about the percentage here:
brainly.com/question/92258
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