Answer:
60%
Step-by-step explanation:
3/5 likely, because there are five hours when the repairman could show up.
Three of them will have the homeowner, and 2 would not. 3/5=0.6=60%
Answer:
Speed of river's current = 5 mph
Step-by-step explanation:
Let 'd' be the distance covered
Let x be the speed of the rivers current
Speed upstream = 15-x
speed downstream = 15+x
Time = distance / speed
time upstream = ![\frac{d}{15-x}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7B15-x%7D)
time downstream = ![\frac{d}{15+x}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7B15%2Bx%7D)
the ferry trip upstream takes twice as long as its return trip downstream
= ![\frac{2d}{15+x}](https://tex.z-dn.net/?f=%5Cfrac%7B2d%7D%7B15%2Bx%7D)
divide both sides by d
= ![\frac{2}{15+x}](https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B15%2Bx%7D)
cross multiply
![15+x= 2(15-x)](https://tex.z-dn.net/?f=15%2Bx%3D%202%2815-x%29)
![15+x= 30-2x](https://tex.z-dn.net/?f=15%2Bx%3D%2030-2x)
Add 2x on both sideds
![15+3x= 30](https://tex.z-dn.net/?f=15%2B3x%3D%2030)
subtract 15 from both sides and divide by 3
![3x=15](https://tex.z-dn.net/?f=3x%3D15)
x=5
Speed of river's current = 5 mph
Answer:
.
Step-by-step explanation:
Answer:
You should expect to find the middle 98% of most head breadths between 3.34 in and 8.46 in.
Step-by-step explanation:
When the distribution is normal, we use 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 question:
![\mu = 5.9, \sigma = 1.1](https://tex.z-dn.net/?f=%5Cmu%20%3D%205.9%2C%20%5Csigma%20%3D%201.1)
In what range would you expect to find the middle 98% of most head breadths?
From the: 50 - (98/2) = 1st percentile.
To the: 50 + (98/2) = 99th percentile.
1st percentile:
X when Z has a pvalue of 0.01. So X when Z = -2.327.
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![-2.327 = \frac{X - 5.9}{1.1}](https://tex.z-dn.net/?f=-2.327%20%3D%20%5Cfrac%7BX%20-%205.9%7D%7B1.1%7D)
![X - 5.9 = -2.327*1.1](https://tex.z-dn.net/?f=X%20-%205.9%20%3D%20-2.327%2A1.1)
![X = 3.34](https://tex.z-dn.net/?f=X%20%3D%203.34)
99th percentile:
X when Z has a pvalue of 0.99. So X when Z = 2.327.
![Z = \frac{X - \mu}{\sigma}](https://tex.z-dn.net/?f=Z%20%3D%20%5Cfrac%7BX%20-%20%5Cmu%7D%7B%5Csigma%7D)
![2.327 = \frac{X - 5.9}{1.1}](https://tex.z-dn.net/?f=2.327%20%3D%20%5Cfrac%7BX%20-%205.9%7D%7B1.1%7D)
![X - 5.9 = 2.327*1.1](https://tex.z-dn.net/?f=X%20-%205.9%20%3D%202.327%2A1.1)
![X = 8.46](https://tex.z-dn.net/?f=X%20%3D%208.46)
You should expect to find the middle 98% of most head breadths between 3.34 in and 8.46 in.
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