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
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Dilation is the trasformation where the figure changes size
Answer: ![\large\boxed{\text{No Solution}}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7B%5Ctext%7BNo%20Solution%7D%7D)
Step-by-step explanation:
<u>Given equation</u>
![\sqrt{t+1}+9=7](https://tex.z-dn.net/?f=%5Csqrt%7Bt%2B1%7D%2B9%3D7)
<u>Subtract 9 on both sides</u>
![\sqrt{t+1}+9-9=7-9](https://tex.z-dn.net/?f=%5Csqrt%7Bt%2B1%7D%2B9-9%3D7-9)
![\sqrt{t+1}=-2](https://tex.z-dn.net/?f=%5Csqrt%7Bt%2B1%7D%3D-2)
<u>Conclusion</u>
![\text{Since radical values are always positive, it is false that }\sqrt{t+1}\text{ will equal to -2}](https://tex.z-dn.net/?f=%5Ctext%7BSince%20radical%20values%20are%20always%20positive%2C%20it%20is%20false%20that%20%7D%5Csqrt%7Bt%2B1%7D%5Ctext%7B%20will%20equal%20to%20-2%7D)
![\text{Therefore, it is }{\large\boxed{\text{No Solution}}}\text{ in the context of real numbers}](https://tex.z-dn.net/?f=%5Ctext%7BTherefore%2C%20it%20is%20%7D%7B%5Clarge%5Cboxed%7B%5Ctext%7BNo%20Solution%7D%7D%7D%5Ctext%7B%20in%20the%20context%20of%20real%20numbers%7D)
Hope this helps!! :)
Please let me know if you have any questions
Answer:
the price of each pound of pretzels is 4.20
Step-by-step explanation
<em> 1 pound · </em>
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