Answer:
The longest braking distance one of these cars could have and still be in the bottom 1% is of 116.94 feet.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean
and standard deviation
, the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
The braking distances of a sample of cars are normally distributed, with a mean of 129 feet and a standard deviation of 5.18 feet.
This means that ![\mu = 129, \sigma = 5.18](https://tex.z-dn.net/?f=%5Cmu%20%3D%20129%2C%20%5Csigma%20%3D%205.18)
What is the longest braking distance one of these cars could have and still be in the bottom 1%?
This is the 1st percentile, which is 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 - 129}{5.18}](https://tex.z-dn.net/?f=-2.327%20%3D%20%5Cfrac%7BX%20-%20129%7D%7B5.18%7D)
![X - 129 = -2.327*5.18](https://tex.z-dn.net/?f=X%20-%20129%20%3D%20-2.327%2A5.18)
![X = 116.94](https://tex.z-dn.net/?f=X%20%3D%20116.94)
The longest braking distance one of these cars could have and still be in the bottom 1% is of 116.94 feet.
Answer:
19
Step-by-step explanation:
11 - 3x < 53
First, subtract 11 from both sides.
-3x < 42
Then divide -3 by both sides, and switch the sign.
x > -14
Answer:
The Domain interval notation is -2 < t < 98
Step-by-step explanation:
The given parameters are;
The time at which the plant began spouting = 2 days before Amy bought it
The number of days the plant was with Amy = 98 days
The maximum height reached by the plant = 30 centimetres
Given that the height of the plant is represented by the function h(t), where h is in centimetres and t is the number of days from the time she bought the plant
Therefore, we have;
At t = -2, h = 0
At t = 98, h = 30
The slope of the function is therefore;
m = (30 - 0)/(98 - (-2)) = 0.3 cm/day
The equation of the function is therefore;
h - 30 = 0.3 × (t - 98)
h = 0.3·t -29.4 + 30 = 0.3·t + 0.6
h(t) = 0.3·t + 0.6
At h(t) = 0, t = -2
At h(t) = 30, t = 98
The interval notation of the domain is therefore, -2 < t < 98.