Answer:
Top 3%: 4.934 cm
Bottom 3%: 4.746 cm
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.
In this problem, we have that:
![\mu = 4.84, \sigma = 0.05](https://tex.z-dn.net/?f=%5Cmu%20%3D%204.84%2C%20%5Csigma%20%3D%200.05)
Top 3%
Value of Z when Z has a pvalue of 1 - 0.03 = 0.97. So X when Z = 1.88.
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![1.88 = \frac{X - 4.84}{0.05}](https://tex.z-dn.net/?f=1.88%20%3D%20%5Cfrac%7BX%20-%204.84%7D%7B0.05%7D)
![X - 4.84 = 0.05*1.88](https://tex.z-dn.net/?f=X%20-%204.84%20%3D%200.05%2A1.88)
![X = 4.934](https://tex.z-dn.net/?f=X%20%3D%204.934)
Bottom 3%
Value of Z when Z has a pvalue of 0.03. So X when Z = -1.88.
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![-1.88 = \frac{X - 4.84}{0.05}](https://tex.z-dn.net/?f=-1.88%20%3D%20%5Cfrac%7BX%20-%204.84%7D%7B0.05%7D)
![X - 4.84 = 0.05*(-1.88)](https://tex.z-dn.net/?f=X%20-%204.84%20%3D%200.05%2A%28-1.88%29)
![X = 4.746](https://tex.z-dn.net/?f=X%20%3D%204.746)
Answer:
B. 10 + 4x ≤ 200
Step-by-step explanation:
From the calculation below, the probability that a tourist will spend more than $250 on the 2 legs of the trip is 2/3.
<h3>How do we calculate the amount spent using probability?</h3>
From the question, the number of possible options available and their total amount is as follows:
Airplane and Van = $350 + $60 = $410
Airplane and Cab = $350 + $40 = $390
Bus and Van = $150 + $60 = $210
Bus and Cab = $150 + $40 = $190
Train and Van = $225 + $60 = $285
Train and Cab = $225 + $40 = $265
From the above, it can be observed that we have a total number of 6 different options available and 4 of the options are more than $250.
Therefore, we have:
Probability of spending more than $250 = Number of options that are more than $250 / Total number of different options = 4/6 = 2/3
Learn more about probability here: brainly.com/question/11034287.
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Answer:
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Step-by-step explanation:
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Answer:
245.10
Step-by-step explanation:
You have to multiply $6.45 by 38