PLEASE HELP ME!I have a really hard time with algebra 2 and I really need to pass:(
1 answer:
Answer:
First problem:
Limiting the Domain to (option A in the list)
Second problem:
All the three statements are true, so pick option D)
Step-by-step explanation:
Recall that a function in order to have inverse needs to be a one-to-one function. In the case of the function they give you in the problem:
the graph corresponds to a parabola with vertex at x=0 and y=1 (0, 1), and since it has two branches that correspond to equal y-values for opposite pairs of x values, it doesn't satisfy the conditions for the existence of inverse. But if we limit the Domain of it considering just one half of the graph (for example limiting the Domain to the values to one side of the parabola's vertex, then this restricted function is one-to-one and we can find its inverse.
So the option of limiting the Domain to x-values smaller than or equal to zero, suggested in option A of the list of answers will do the job we need.
In the following problem, the three first statements are true for an inverse function, so pick option D that says that all previous statements are true.
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Answer:
a) By the Central Limit Theorem, it is approximately normal.
b) The standard error of the distribution of the sample mean is 1.8333.
c) 0.1379 = 13.79% of the samples will have a mean useful life of more than 38 hours.
d) 0.7939 = 79.39% of the samples will have a mean useful life greater than 34.5 hours
e) 0.656 = 65.6% of the samples will have a mean useful life between 34.5 and 38 hours
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
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:
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.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean of 36 hours and a standard deviation of 5.5 hours.
This means that
a. What can you say about the shape of the distribution of the sample mean?
By the Central Limit Theorem, it is approximately normal.
b. What is the standard error of the distribution of the sample mean? (Round your answer to 4 decimal places.)
Sample of 9 means that . So
The standard error of the distribution of the sample mean is 1.8333.
c. What proportion of the samples will have a mean useful life of more than 38 hours?
This is 1 subtracted by the pvalue of Z when X = 38. So
By the Central Limit Theorem
has a pvalue of 0.8621
1 - 0.8621 = 0.1379
0.1379 = 13.79% of the samples will have a mean useful life of more than 38 hours.
d. What proportion of the sample will have a mean useful life greater than 34.5 hours?
This is 1 subtracted by the pvalue of Z when X = 34.5. So
has a pvalue of 0.2061.
1 - 0.2061 = 0.7939
0.7939 = 79.39% of the samples will have a mean useful life greater than 34.5 hours.
e. What proportion of the sample will have a mean useful life between 34.5 and 38 hours?
pvalue of Z when X = 38 subtracted by the pvalue of Z when X = 34.5. So
0.8621 - 0.2061 = 0.656
0.656 = 65.6% of the samples will have a mean useful life between 34.5 and 38 hours