Exponential function f is represented by the table. x -1 0 1 2 3 4 f(x) 7.5 7 6 4 0 -8 Function g is an exponential function pas
sing through the points (0,27) and (3,0). Which statement correctly compares the behavior of the two functions on the interval (0, 3)? A. Both functions are positive and decreasing on the interval. B. Both functions are positive on the interval, but one function is increasing while the other is decreasing. C. Both functions are positive and increasing on the interval. D. One function is positive on the interval, and the other is negative.
1 answer:
Answer:
A. Both functions are positive and decreasing on the interval.
Step-by-step explanation:
The table shows that f(x) decreases when x increases in the interval (0,3).
All the values of f(x) are positive in the interval (0,3).
For the exponential function that passes through the points (0, 27) and (3, 0), we also see that f(x) is decreasing when x increases: when x goes from 0 to 3, f(x) goes from 27 to 0.
Also all the values of f(x) are positive in the interval.
Then, both functions are positive and dereasing in the interval.
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Answer:
a) 0.27% probability that the mean is less than 1995 milliliters.
b) 2002.3 milliliters or more will occur only 10% of the time for the sample of 100 bottles.
Step-by-step explanation:
To solve this problem, it is important to understand the normal probability distribution and the central limit theorem
Normal probability distribution
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:
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.
Central Limit theorem
The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation
, a large sample size can be approximated to a normal distribution with mean
and standard deviation
In this problem, we have that:
A) If the manufacturer samples 100 bottles, what is the probability that the mean is less than 1995 milliliters?
So
This probability is the pvalue of Z when X = 1995. So
By the Central Limit Theorem
has a pvalue of 0.0027
So 0.27% probability that the mean is less than 1995 milliliters.
B) What mean overfill or more will occur only 10% of the time for the sample of 100 bottles?
This is the value of X when Z has a pvalue of 1-0.1 = 0.9.
So it is X when
2002.3 milliliters or more will occur only 10% of the time for the sample of 100 bottles.