Answer:
<u>C</u><u>A</u><u>R</u><u>R</u><u>Y</u><u> </u><u>O</u><u>N</u><u> </u><u>L</u><u>E</u><u>A</u><u>R</u><u>N</u><u>I</u><u>N</u><u>G</u><u> </u><u>B</u><u>E</u><u>G</u><u>G</u><u>I</u><u>N</u><u>E</u><u>R</u><u> </u><u>P</u><u>A</u><u>L</u><u>A</u><u>N</u><u>G</u><u> </u><u>P</u><u>O</u><u> </u><u>K</u><u>A</u><u>S</u><u>I</u><u> </u><u>A</u><u>K</u><u>O</u><u> </u><u>E</u><u>H</u>
Step-by-step explanation:
sorry po
Using the normal distribution, it is found that there is a 0.0436 = 4.36% probability that a randomly selected caterpillar will have a length longer than (greater than) 4.0 centimeters.
<h3>Normal Probability Distribution</h3>
The z-score of a measure X of a normally distributed variable with mean
and standard deviation
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 above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
In this problem, the mean and the standard deviation are given, respectively, by:
.
The probability that a randomly selected caterpillar will have a length longer than (greater than) 4.0 centimeters is <u>one subtracted by the p-value of Z when X = 4</u>, hence:
![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{4 - 2.8}{0.7}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7B4%20-%202.8%7D%7B0.7%7D)
Z = 1.71
Z = 1.71 has a p-value of 0.9564.
1 - 0.9564 = 0.0436.
0.0436 = 4.36% probability that a randomly selected caterpillar will have a length longer than (greater than) 4.0 centimeters.
More can be learned about the normal distribution at brainly.com/question/24663213
#SPJ1
Pretty sure it’s A sorry if that’s wrong
Answer:
7
Step-by-step explanation:
If you plug in the variable for x and y you get:
5+3-1
Use the order of operations to solve:
5+3-1
8-1
7
Answer:
- width: 18 in
- length: 27 in
Step-by-step explanation:
The relations between length (L) and width (W) are ...
W +9 = L
LW = 486
Substituting gives ...
(W+9)W = 486
W^2 +9W -486 = 0 . . . put in standard form
(W +27)(W -18) = 0 . . . . factor
W = 18 . . . . the positive solution
The width of the rectangle is 18 inches; the length is 27 inches.
_____
<em>Comment on factoring</em>
There are a number of ways to solve quadratics. Apart from using a graphing calculator, one of the easiest is factoring. Here, we're looking for factors of -486 that have a sum of 9.
486 = 2 × 3^5, so we might guess that the factors of interest are -2·3² = -18 and 3·3² = 27. These turn out to be correct: -18 +27 = 9; (-18)(27) = -486.