Answer:
A. 637
B. 0.2240 (4 dp) = 22.4% (nearest tenth)
Step-by-step explanation:
<u>Normal Distribution</u>
![\sf X \sim N(\mu, \sigma^2)](https://tex.z-dn.net/?f=%5Csf%20X%20%5Csim%20N%28%5Cmu%2C%20%5Csigma%5E2%29)
Given:
![\implies \sf X \sim N(190.6, 5.8^2)](https://tex.z-dn.net/?f=%5Cimplies%20%5Csf%20X%20%5Csim%20N%28190.6%2C%205.8%5E2%29)
<h3><u>Part A</u></h3>
![\begin{aligned}\sf P(180 < X < 190) & = \sf P(X < 190)-P(X\leq 180)\\& = \sf 0.4588035995-0.03380583874\\& = \sf 0.4249977608\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Csf%20P%28180%20%3C%20X%20%3C%20190%29%20%26%20%3D%20%5Csf%20P%28X%20%3C%20190%29-P%28X%5Cleq%20180%29%5C%5C%26%20%3D%20%5Csf%200.4588035995-0.03380583874%5C%5C%26%20%3D%20%5Csf%200.4249977608%5Cend%7Baligned%7D)
Total number of bodybuilders = 1500
Therefore, the number of bodybuilders between 180 and 190 pounds is:
![\begin{aligned}\sf P(180 < X < 190) \cdot1500 & = \sf 0.4249977608 \cdot 1500\\& = \sf 637.4966412\\& = \sf 637\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Csf%20P%28180%20%3C%20X%20%3C%20190%29%20%5Ccdot1500%20%26%20%3D%20%5Csf%200.4249977608%20%5Ccdot%201500%5C%5C%26%20%3D%20%5Csf%20637.4966412%5C%5C%26%20%3D%20%5Csf%20637%5Cend%7Baligned%7D)
<h3><u>Part B</u></h3>
![\begin{aligned}\sf P(X > 195) & = \sf 1-P(X\leq 195)\\& = \sf 1-0.7759602537\\ & = \sf 0.2240397463\\ & = \sf 0.2240\:(4\:dp)\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Csf%20P%28X%20%3E%20195%29%20%26%20%3D%20%5Csf%201-P%28X%5Cleq%20195%29%5C%5C%26%20%3D%20%5Csf%201-0.7759602537%5C%5C%20%26%20%3D%20%5Csf%200.2240397463%5C%5C%20%26%20%3D%20%5Csf%200.2240%5C%3A%284%5C%3Adp%29%5Cend%7Baligned%7D)
0.2 would be 20% written as a decimal.
That is the simplest form.
Answer:
The answer is 1
Step-by-step explanation:
You can use the formula, a²-2ab+b² = (a-b) to evaluate the following question:
899² - 2(899)(898) + 898² = (899-898)²
= 1
(Hooe this can help)
Answer:
-7 units
Step-by-step explanation:
count -7 units